An object has a mass m = 0.4kg. It is attached to a spring that has spring const

Question

An object has a mass m = 0.4kg. It is attached to a spring that has spring constant of k = 75N/m. At time t = 0 the object is pulled to a distance of 10 cm from its equilibrium position (which you may choose conveniently at x = 0). The surface on which the object moves is frictionless. (Assume the motion is horizontal.) What force does the spring exert on the object just before it is released? (Assume the positive direction is the direction in which the object is pulled before it is released. Indicate the direction with the sign of your answer.) What are the angular frequency, the frequency, and the period of the oscillation? What is the amplitude of the oscillation? What is the maximum speed of the object?

Explanation / Answer

Force applied=-kx

where k=spring constant=75 N/m

x=0.10 m

So, force,F=75*0.1=7.5 N

Period,T=2*pi*(m/k)1/2

mass,m=0.4 kg

k=75 N/m

So, T=2*3.14*(0.4/75)0.5=0.458 s

Angular frequency,w=2*3.14/T=13.69 rad/s

frequency,f=1/T=2.183 Hz

x=Asinwt

Amplitude,A=x/sinwt

A=0.10/sin(13.69*0.458)=0.916 m

Maximum speed,v=Aw

A=amplitude

w=angular frequwncy,

So v=0.916*13.69=12.53 m/s

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