An empty box is attached to a horizontal spring on a frictionless floor. Pull th

Question

An empty box is attached to a horizontal spring on a frictionless floor. Pull the block a few feet to the right to stretch the spring, and let go so that the box oscillates on the spring. Then you do this: Exactly at the moment when the box is at the far right end of its path (where its speed is momentarily zero), you drop a bag of sand into the box. (The sand has the same mass as the box.)

a) Does the amplitude of the oscillations increase, decrease, or stay the same? Why?

b) Does the frequency of the oscillations increase, decrease, or stay the same? Why?

c) Does the maximum speed of the box increase, decrease, or stay the same? Why?

Explanation / Answer

Solution) in oscillation the amplitude do not depend on mass so it remains the same

It is given by Y=Asin(wt+p)

From above it do not depend on mass

(b) frequency f=(1/(2pi)(k/m)^(1/2)

So frequency is inversely proportional to mass so as mass increases frequency decreases.

So here frequency decreases

(c) Maximum speed is v=Aw

So it do not depend on mass so it remains constant .

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