During the blowing of the Shofar on Rosh Hashanah we accept upon ourselves Hashem as our King as mentioned in Rosh Hashana 16 -
אמרו לפני בראש השנה מלכיות זכרונות ושופרות מלכיות כדי שתמליכוני עליכם זכרונות כדי שיעלה זכרוניכם לפני לטובה ובמה בשופר

The gemarah adds that the reason we blow the shofar of a ram is because it reminds Hashem of the merit of the Akeidas Yitzchak and thereby it is deemed as if every individual also was bound as a sacrifice to Hashem.

אמר רבי אבהו למה תוקעין בשופר של איל אמר הקדוש ברוך הוא תקעו לפני בשופר של איל כדי שאזכור לכם עקידת יצחק בן אברהם ומעלה אני עליכם כאילו עקדתם עצמכם לפני

Why is it that the source of the coronation of Hashem as one's king on Rosh Hashanah connects specifically to the Akaidah?

The mitzvah of Blowing Shofar requires from the Torah to blow תקיעה תרועה תקיעה three times. What should these three particular sounds mean to us? We suggest the following interpretation. Avraham was the pillar of chesed in the world, in contrast to Yitzchak who personified the pillar of din judgment. At the Akaidah, Avraham was tested in the middah of yirah, the opposite extreme middah in which he excelled during his lifetime, chesed. The command from Hashem was extremely challenging to Avraham from many aspects. Hashem was demanding from him a human sacrifice which that alone was contrary to the belief that he preached to the masses all these years that Hashem despises human sacrifice. Furthermore, the human sacrifice was to be his only son who was the future of Am Yisrael. The challenge of this test was further made difficult because to kill is an act of Middas Hadin the complete opposite of Avraham's Pillar Middah of Chesed. However, Avraham's devoted and unflinching dedication to the service of Hashem propelled him to execute his command completely would it not have been that at the very last second he was stopped by a malach in the name of Hashem.

Hashem tells Avraham that now after seeing him overpower these very difficult challenges He knows that he is ירא אלקים G-d fearing par excellence. But there is also another aspect that was revealed with this test. A person could be a Baal Chesed because he naturally is a good hearted person and he was born that way. Or it could originate from nurturing and chinuch. This fundamental is expounded upon by the Alter from Slabodka ztl when analyzing the zechus that Lot possessed in order to be saved from the complete destruction of Sodom.

Chazal say it was because when he was asked what relationship Avraham have with Sarah, whether it was his wife or sister like Avraham claimed, he said it was his sister. Had he told the truth they would have killed Avraham and taken his wife to Pharaoh as a King's prize. The Alter asked why wasn't the chesed of Lot in his incredible demonstration of the mitzvah of Hachnasos Orchim valued and sufficient to merit redemption? After all when the riot crowd of Sodom charged his house to take away his guests with the intention of evil, Lot stood in the doorway and risked his life in order to protect them.

The Alter answered that this great degree to perform of Hachnasas Orchim even with mesiras nefesh was a learned behavior from his great Rebbi Avraham Avinu which he saw demonstrated in his dwelling constantly. Such a learned conduct doesn't describe the virtuous essence of an individual especially when his life is in danger of being lost. However, the fact that Lot loved money and he was willing to forfeit a large sum from received from the Egyptians if he would have just given the honest information to them that Sarah was really his wife, this was cherished as the merit that came to save his life. It was his willingness to lose a great wealth by not saying the "truth" and it was considered one of Lot's greatest challenges that he overcame.

So too, by the acts of Avraham's chesed. One might question, who said that he excelled to become the Pillar of chesed because of choice and reached the levels of excellence because he was emulating Hashem's ways. Maybe it was because of his inner born natural good heartedness which then it doesn't make him so virtuous. The proof of Avraham's greatness emerged when at the Akaidah test Hashem asked him to do the unthinkable to bring a human sacrifice by slaughtering his only son that he alone was capable of continuing the destiny of Hashem's future nation. By attaining a pinnacle level of Yirah of Hashem which he never possessed up until now, and acting with the opposite extreme from his giant middah of chesed, this reflected that even the chesed that he fulfilled during his lifetime was also his own self achievement and not nurtured or natured. Without his true deep dedication and love of Hashem, Avraham would not have been able to overcome this challenge and go completely against his life's teachings and his superior middah of chesed. This could not be possible if his attribute of chesed was only gifted to him from a source other than his own.

So now after the Akeidah we find Avraham excelling with two pillars, chesed ahavah\ and din \ yirah. Avraham hinted to Yitzchak of this scenario happening when he said to Yitzchak as they reached the top of Har Hamoriya their destination, הנני בני behold I am ready my son. The word בני seems superfluous. Therefore it is to be interpreted that Avraham was for the last three days processing and perfecting the madraiga of Yitzchak's Yirah needed in order to fulfill his mission. It incredibly reached the point where he said הנני בני behold I am holding at being the madraigah of my son.

Let us not forget that during the same time in his spiritual journey to acquire Middas Hadin, Avraham also strove to preserve his exemplary Pillar Midda of chesesd to ensure that it won't be affected nor compromised an iota because of his incredible upgrade and shelaimus with the extreme opposite middah of yirah.

With this we can understand the passuk 22,17 כי ברך אברכך and Rashi comments אחת לאב ואחת לבן that the double blessing refers to a berachah to the father and a beracha to the son. Yet the lashon is singular as if Hashem was speaking only to Avraham and his two berachos? According to our above explanation, in truth, both berachos paralleled Avraham's achievements at the Akaida for the two middos that he perfected. The Av Middah was his chesed Pillar that he perfected up until now and which was preserved in full form without any compromise. The son beracha was a reward for attaining the madraiga of Yitzchak who excelled with yirah to an extreme madraigah.

With this we can also answer the statement of Avraham to Yishmael and Eliezer who accompanied them on the mission "we are going yonder ונשובה אליכם we will return to you". However the passuk says clearly 22,19 וישב אברהם אל נעריו that only Avraham returned and not Yitzchak? The answer is that Avraham was referring to his new acquirement of Yitzchak's midda of yirah כי ירא אלקים אתה the transition of הנני בני behold I am my son. I am carrying in me the outstanding Pillar Middah of my son as well, and therefore it is understood his usage of the plural "we".

The Radziner Rebbe ztl describes the avoda of a Yid during his lifetime by comparing it to an individual who has a canoe with only one oar and he wants to get to the other bank of the river. In order to do so, he must paddle on the right side of the canoe and also on the left. For if the paddling is only on one side exclusively, no matter how strong he paddles he will find himself in circles in the same place. The right side symbolizes chesed and ahava, the left din and yirah. To serve Hashem properly one must be the baal habayis over his middos in order that he will be flexible and be able to switch from middah to middah by always taking cues from Hashem what middah is the right choice. As Rav Tzadok from Lublin wrote in his sefer Kometz Hamincha
אות כב אין לאדם לשום התכלית ומכוון לאיזה דבר פרטי רק צופים בכל עת בבינה שבלב לדעת מה רצון השם יתברך באותה עת מה יעשה ישראל. וזהו מבני יששכר יודעי בינה לעתים לדעת מה יעשה. וזהו לך לך מארצך בראשית יב א רצה לומר ממקום שקבעת לך שאתה רוצה לעשות חסד לבריות וכיוצא שלא יהיה לך מקום מוגבל שלך רק אל הארץ אשר אראך שיהיה מקומך ומדוררך אשר אראך אשר אני מראה אותך בכל עת ובכל רגע אני מראה אותך זהו ארצי ומקומי שם תדור עכ"ד.

On Rosh Hashana we seek the merit of the Akaidah through which we blow shofar and accept Hashem's Kingdom upon ourselves. The way we accept Hashem's kingdom is by bringing awareness of Avraham's nisayon and achievements during his final test of completing self - control over his shelaimus hamiddos of chesed and din. We too must strive to be the baal habos over our middos and not vice versa merely to react to situations without prior contemplation. Sometimes we must be tough and at other times soft, holding our ground or being mevatair, being strict upon ourselves and in other occasions lenient, all depending upon what is the ratzon of the Melech at each particular situation.

Chazal derive from the shofar blowing of Yom Kippur on Yovel, when all Jewish slaves must be set free, that the sounds blown are tekiah, a long blast, a teruah a broken blast and once again a long blast (repeated three times). The shofar of the ram is used not only to connect Rosh Hashanah with the Akaidah merit but also as a directive manual how to accept Hashem's Kingship as Avraham did during his test. The tekiah sound corresponds to the middah of chesed for it is extended and connected אהבה גמטריא .אחד Avraham came to the Akaida with an exemplary status of the Pillar of Chesed and ahavas Hashem. At the Akaida he reached another completion of a middah that of Yizchak, symbolized by the תרועה the broken sound, smaller pieces disconnected from each other עתה ידעתי כי ירא אלקים אתה. However, by reaching the shelaimus of yirah by going against his self earned establishment of chesed, it also demonstrated the shelaimus of his Middas Chesed that was achieved only because of fulfilling the ratzon of Hashem to emulate Him and not because of nature or nurture. This represents the second tekiah following the teruah the revealing of Avraham's shelaimus in the middah of chesed which was not compromised even though he achieved a shelaimus in the middah of yirah at the same time.

The shofar of Rosh Hashanah is a call for every Yid to seek liberty (Yovel) and not allow himself to be enslaved to any particular middah even if it is a good and noble one. Being an eved to Hashem is the ability to inquire what does Hashem want from me right now and not only what is my good middah telling me to do. My Rebbi ztl told us this story more than once about an Avreich who was makpid to hear Kerias Megillas Esther from a megilla with a particular number of lines on each page. In order to make that one particular minyan in the morning, he warned his wife that as soon as she finishes her early minyan she should immediately come home so he wouldn't miss his minyan. Their family was composed of a new born baby with five other siblings all under the age of eight. His wife got stuck in a traffic jam and she arrived home forty minutes later. Her husband was not home for he had left to make his minyan leaving the family and house in absolute chaos and wreck. All six children were traumatized and hysterical. Do you think for a moment that Hashem desired this Avreich's chumrah at the expense of his children's trauma!

The gemarah in Taanis 20b says
מיד נכנס רבי אלעזר בן רבי שמעון ודרש לעולם יהא אדם רך כקנה ואל יהא קשה כארז ולפיכך זכה קנה ליטול הימנה קולמוס לכתוב בו ספר תורה תפילין

A person should forever be soft and flexible like a reed that can bend in either direction. Therefore it merited to be used as a pen to write the parshiyos of tefillin and a sefer Torah.