An object is in simple harmonic motion. Find an equation for the motion given that the frequency is 3⁄π and at time t = 0, y = 0, and y' = 6. What is the equation of motion?

Answer: y (t) = 1/π^2 sin (6*π^2*t)

Explanation:

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Answer: y (t) = 1/π^2 sin (6*π^2*t)

Explanation: In order to solve this problem we have to consider the general expression for a harmonic movement given by:

y (t) = A*sin (ω*t + φo) where ω is the angular frequency. A is the amplitude.

The data are: ν = 3π; y (t=0) = 0 and y' (0) = 6.

Firstly we know that 2πν=ω then ω=6*π^2

Then, we have y (0) = 0=A*sin (6*π^2*0+φo) = A sin (φo) = 0 then φo=0

Besides y' (t) = 6*π^2*A*cos (6*π^2*t)

y' (0) = 6=6*π^2*A*cos (6*π^2*0)

6=6*π^2*A then A = 1/π^2

Finally the equation is:

y (t) = 1/π^2 sin (6*π^2*t)