A massless spring with spring constant k is attached at one end of a block of ma

Question

A massless spring with spring constant k is attached at one end of a block of mass M that is resting on a frictionless horizontal table. The other end of the spring is fixed to awall. A bullet of mass mb is fired into the block from the left with a speed v0 and comesto rest in the block. (Assume that this happens instantaneously).

The resultion motion of the block and the spring is simple harmonic motion.

.....................|||||||||||||||||       (spring) K      |

...... ..............| (block) M +m_b   |;,.:"":;,,;:"':;,,;"';;,|

________|______|_______________|_________________| <-------(this flat line is the frictionless table)

              |--------------->|

       x = 0            x

(Sorry for the weird looking diagram.... the "custom diagram" feature keeps erasing it every time make one. I hope this one is sufficient).

QUESTIONS:

a) Find the amplitude of the resulting simple harmonic motion.

b) How long does it take the block to first return to the position x = 0 ?

c) What fraction of the original kinetic energy of the bullet is stored in the harmonicoscillator?

(ANSWER TO ALL PARTS WILL RESULT IN A LIFESAVER RATING. THANK YOU)

Explanation / Answer

a) T=2*pi*((M+mb)/k)^1/2 is the period : Amax=(mus(M+mb)*g)/k or "d*(M/(M+mb))^1/2 in this formula k amplitude is independent of k here" k is in N/m b) y=A*cos omega*t omega=(k/m)^1/2 in rad/s c) k=1/2*m*v^2=1/2*m*omega^2*A^2*sin^2*(omega*t+phi) mb/(M+mb)*100

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