Question

Could someone show me how to work this? It's for a study guide I'm practicing, and I just can't seem to get the correct answer.

The position of a 0.63 kg object attached to a spring is described by [x = (1.09 m) cos(3.11πt)]

a) Find the object’s position at t = 1.09 s. Answer in meters.


b) Find the object’s acceleration at the same time. Answer in m/s2.


c) What is the frequency of oscillations in Hz?


d) What is the period of oscillations in s?

I've tried using d=x*t for the first part, but I think I must be missing something. This is more advanced stuff than I'm used to so I'm not sure how to go about it

Answer 1

For part a)
Just substitute in t into the equation you have.
x = (1.09)cos(3.11πt)
x is the displacement and this will come out as an answer in meters. 1.09m is your max amplitute (the number in front of the cos). If you get a negative answer that just means the spring is being compressed so you get a negative displacement

for part b)

I think for this because you have x in terms of t, dx/dt = velocity and dv/dt = acceleration. So if you get d2x/dt2 (the second derivitive) of

(1.09)cos(3.11πt)

and then substitute in the value of t you have for part a) you'll get the acceleration

for part c)

For SHM x = (A)cos(2πt/T)
where t = time and T = period

put 2πt/T = 3.11πt and solve for T

for part d) Frequency = one over the period or

f = 1/T

Answer 2

I'm not getting the right answer for part b. Could someone help me understand this part better?