A 200 g mass attached to a horizontal spring oscillates at a frequency of 2 Hz. At one instant the mass is at x=5 cm and has a Vx=-30 cm/s.Determine:

a) the period ( i got T=.5s)
b) the amplitude
c) the max speed
d) the total energy

need equations to solve this, please help.

1 answer

First determine the spring constant, k. Use this equation:

Period = 2*pi*sqrt(m/k)= 0.5 s

Next compute the total energy at the starting time, using the given values of X (0.05m) and V (-0.3 m/s)at that time. That will be the answer to part (d)

Etotal = (1/2) kX^2 + (1/2) M V^2

Then compute the amplitude Xmax by setting
(1/2)kXmax^2 = Etotal

get the maximum speed Vmax by setting
Etotal = (1/2) M Vmax^2
and solving for Xmax

Etotal = (1/2) k X^2 + (1/2) M V^2