Question

A 0.5 kg mass vibrates with an amplitude of 0.7 m and a frequency of 5 Hz. If the mass is located at the amplitude position at t = 0, moving with a positive velocity, determine: a. b. The equation of motion describing the system: the total energy of the system. The velocity of the mass as it moves through the equilibrium position c.

Answer 1

a]

Since the motion starts from Aplitude position

A=Amplitude= 0.7m

w=Angular Velocity= 2$\pi$f= 10$\pi$

At t=0, x=A

x=Acos(wt)= 0.7cos(10$\pi$t)

x= 0.7cos(10$\pi$t)

b]

TE=Total Energy

TE= 1/2mA²w²= 1/2*0.5*(0.7)²*(10$\pi$)²= 120.90 Joules

c]

V=Velocity is maximum at equlibrium position= Aw

V=Aw

V= 0.7*10$\pi$=  21.991$\approx$ 22 m/s