# 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.

## Tutor Answer

## Review from our student for this Answer

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors