Question

50 POINTS!
Only help if you know how to do the problem please.

Answer 1

The position equation will be:

`y(t)=2sin((2\pi)/(3) t)`

Explanation:

The general position equation of mass attached to a spring is given by:

`y(t)=Asin(\omega t-\phi)`

Where:

• A is the amplitude of the sinusoidal motion
• ω is the angular frequency (ω=2πf)
• ∅ is the phase (zero in our case)

We know that it takes 3 sec for the spring to complete one cycle. It means the period is T = 3 s.

Let's recall that T = 1/f where f is the frequency, so f = 1/3 Hz and hence ω=2π(1/3)=2π/3.

The amplitude is the distance from the origin to the crest. In our case, A = 4/2 in = 2 in, because the distance from the highest to the lowest is 4.

Therefore, the position equation will be:

`y(t)=2sin((2\pi)/(3) t)`

I hope it helps you!