Posted: December 30th, 2021

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.

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