Physics Homework Help

1.      A particle with a mass of 3.8 × 10-20 kg is oscillating with simple harmonic motion with a period of 3.1 × 10-5 s and a maximum speed of 2.0 × 103 m/s. Calculate (a) the angular frequency and (b) the maximum displacement of the particle.

2.      A simple harmonic oscillator consists of a block of mass 3.20 kg attached to a spring of spring constant 140 N/m. When t = 2.00 s, the position and velocity of the block are x = 0.137 m and v = 3.040 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?

3.      A block of mass M = 6.20 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k = 5570 N/m. A bullet of mass m = 9.60 g and velocity   of magnitude 570 m/s strikes and is embedded in the block (the figure). Assuming the compression of the spring is negligible until the bullet is embedded, determine (a) the speed of the block immediately after the collision and (b) the amplitude of the resulting simple harmonic motion.

4.      In the figure, a physical pendulum consists of a uniform solid disk (of radius R = 55.6 cm) supported in a vertical plane by a pivot located a distance d = 27.7 cm from the center of the disk. The disk is displaced by a small angle and released. What is the period of the resulting simple harmonic motion?

5.      The 3.50 kg cube in the figure has edge lengths d = 5.10 cm and is mounted on an axle through its center. A spring (k = 1300 N/m) connects the cube’s upper corner to a rigid wall. Initially the spring is at its rest length. If the cube is rotated 5.00° and released, what is the period of the resulting SHM?

6.      A block is in SHM on the end of a spring, with position given by x = xmcos (ω t + φ). If φ = 1.41 rad, then at t = 0 what percentage of the total mechanical energy is potential energy?

7.      What is the phase constant for SMH with a(t) given in the figure if the position function x(t) has the form x = xmcos(ωt + φ) and as = 4 m/s2? (note that the answer should be from 0 to 2π)