Question

b. find the velocity of the oscillator, v(t)=y(t). c. graph the velocity function for 0≤t≤10. v(t) = 36 cos t

Explanation:

Step1: Identify key features of $y = 36\cos t$

The general form of a cosine - function is $y = A\cos(Bt - C)+D$. For $y = 36\cos t$, we have $A = 36$, $B = 1$, $C = 0$, and $D = 0$. The amplitude is $|A|=36$, and the period is $T=\frac{2\pi}{B}=2\pi\approx6.28$.

Step2: Evaluate function at key - points

When $t = 0$, $v(0)=36\cos(0)=36$. When $t=\frac{\pi}{2}$, $v(\frac{\pi}{2})=36\cos(\frac{\pi}{2}) = 0$. When $t=\pi$, $v(\pi)=36\cos(\pi)=- 36$. When $t=\frac{3\pi}{2}$, $v(\frac{3\pi}{2})=36\cos(\frac{3\pi}{2}) = 0$. When $t = 2\pi$, $v(2\pi)=36\cos(2\pi)=36$.

Step3: Analyze the graphs

We are looking for a graph with an amplitude of 36 (the maximum value from the mid - line is 36 and the minimum value from the mid - line is also 36) and a period of approximately 6.28.

Answer:

A.