Question

the position of a mass that is oscillating on a spring is given by x = (0.20m) cos [(5.00s^-1)t]. what is the period of the motion? what is the amplitude of the motion? what is the spring constant? what is the total mechanical energy of the system?

Answer 1

Compare the given equation with the genarl equation shm.

So Amplitude=0.2 m

f=5/s

So w=2 pie/f =2*3.14/5=1.256 rad/s

k=m*w^2=m81.256*1.256

=1.577 m where m is the mass of the body attached with spring.

Total energy = 0.5*k*x^2 at the amplitude

0.5*k*0.2*0.2 Joules.