I order to mix a can of paint with a mass of 2 kg, it is placed on the end of a

Question

I order to mix a can of paint with a mass of 2 kg, it is placed on the end of a spring with a spring constant of 140 N/m and allowed it to move back and forth in simple harmonic motion. The can begins at rest with the spring compressed at a distance of 15 cm. Spring mass is negligable. A)Write equation for the can's displacement as a fuinction of time. B) What's the max speed of the can as it moves. C) At what displacement is th kinetic energy equal to the potential. D) Will the time for one occilation change if the amplitude changes.

Explanation / Answer

here let the equation be

x(t)=Acos(wt+fi)

so at t=0 x'=0 so fi=0

and at t=0 x(t)=0.15 m so A=0.15m

so equation =0.15cos(wt)

where w=sqrt(k/m)=8.366

B) max speed=A*w=1.255 m/s

C) PE=0.5*140*A^2cos^2(wt)=0.5*2*(A^2*w^2)sin^2(wt)

so we get cos(wt)=0.707

so x=0.15*cos(8.366*0.093)=0.106 m

D) Time period does not depend on amplitude so doesnot change

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