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Chapter 15: Q.76 (page 419)
A long, rod is pivoted at one end. A ball of clay is stuck on the other end. What is the period if the rod and clay swing as a pendulum?
Period
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Prove that the expression for in Equation is a solution to the equation of motion for a damped oscillator, Equation , if and only if the angular frequency is given by the expression in Equation .
A block oscillating on a spring has a maximum speed of . What will the block's maximum speed be if the total energy is doubled? Explain.
a. When the displacement of a mass on a spring is , what fraction of the energy is kinetic energy and what fraction is potential energy?
b. At what displacement, as a fraction of A, is the energy half kinetic and half potential?
The head of a bobble-head doll oscillates in SHM at a frequency of .
a. What is the spring constant of the spring on which the head is mounted?
b. The amplitude of the head鈥檚 oscillations decreases to in . What is the head鈥檚 damping constant?
An air-track glider attached to a spring oscillates between the mark and the mark on the track. The glider completes oscillations in . What are the (a) period, (b) frequency, (c) angular frequency, (d) amplitude, and (e) maximum speed of the glider?
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