# Simple Harmonic Motion. How do I find the following?

**Question description**

A mass 1.2 kg of is attached to a spring and placed on a friction-less air track. Initially the mass is resting in equilibrium. A 10-gram bullet is fired into the mass to initiate oscillatory motion. The bullet hits the mass from the left side at a speed of 120 m/s at t=0 and gets lodged inside of it. After that, the system starts oscillating harmonically with a period of 15 seconds.

the initial velocity of the mass right after it was hit by the bullet.

Initial Momentum = m*v = 0.010 * 120 = 1.2

Final momentum = Initial momentum = m * v

v = Initial momentum / m = 1.2 / (1.2 + 0.010) = 0.992 m

the kinetic energy of the bullet, the kinetic energy of the mass right after it

was hit by the bullet

Bullet Kinetic energy: Ek = 1/2 * m * v^2 = 1/2 * 0.010 * 120^2 = 72 J

Mass after bullet strick: Ek = 1/2 * mtotal * v^2 = 1/2 * 1.21 * 0.992^2 = 0.595 J

Using this how do I find the following?

Find the amplitude and phase constant of the resulting oscillations.

Write explicit expressions for the position x(t) and velocity v(t) of the mass as a function of time.

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