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Solve the given problems by integration.The angular velocity $\omega$ (in $\mathrm{rad} / \mathrm{s}$ ) of a pendulum is $\omega=-0.25 \sin 2.5 t .$ Find the angular displacement $\theta$ as a function of $t$ if $\theta=0.10$ for $t=0$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 4

Basic Trigonometric Forms

Integrals

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mhm. We're given the angular velocity here for a pendulum. We want to find angular displacement data given that the third is 0.1 when T goes to zero. Now we know Tito is actually integrating the angular velocity. So it will be integrating minus 0.25 Sign 2.5 T. D. T. No. Let you be 2.5 T. Okay. Mhm. So D you will be 2.5 D. T. So I need 82.5 over here. So I will put a 1/2 0.5. Yeah. Mhm. So I can have a 2.5 here with the tea over here. So this will be my D. U. This is you. I can bring this constant minus 0.25 to outside the integration sign. So minus 0.25 divided by 2.5. I will get minus your 0.1 and I will have signed now over here. This is signed you. And this part here is the you. So now I'm integrating Sine you respect to you. That will be my next call. Sign you. Classy. So my angular displacement is 0.1. Who signed? Now replace the you back with 2.5 T. Privacy. Something when he goes zero. Tita is 0.1. Okay, Hussein zero will be once or C will be zero. So therefore tita is 0.1. Hussein 2.5 T. All right.

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