Question

Instructions:

Write the equations that will be used for each problem and include every algebraic process.

A spring oscillates with the angular frequency of 2 radians / seconds. There is a mass of 0.500 kilograms tied to the dock. The pier stretches about 0.08 meters.

a. Determine the mechanical energy of the mass.

b. Determine the velocity of the object when it passes through the point x = 0.02 meters.

Answer 1

Angular frequency ,=2 rad/s

mass,m=0.500 kg

Amplitude,A=0.08 m

Displacement for spring-mass system is given by

x=Acos(t)

Velocity,v=-Asin(t)

Part a.

Mechanical energy=P.E+K.E=(1/2)kx²+(1/2)mv²

=(1/2)k(Acos(t))²+(1/2)m(Asin(t))²=(1/2)m²A²=(1/2)0.5002²0.08²=6.410^-3 J

Part b

when x=0.02 m

so

0.02=0.08 cos(t)

or

cos(t)=0.25

or

t=75.22⁰

Velocity=-Asin(t)=-0.082sin(75.22)=0.155 m/s