91Ó°ÊÓ

A \(1.0 \mathrm{kg}\) block is attached to a spring with spring constant 16 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of \(40 \mathrm{cm} / \mathrm{s}\) What are a. The amplitude of the subsequent oscillations? b. The block's speed at the point where \(x=\frac{1}{2} A ?\)

A spring is hanging from the ceiling. Attaching a \(500 \mathrm{g}\) physics book to the spring causes it to stretch \(20 \mathrm{cm}\) in order to come to equilibrium. a. What is the spring constant? b. From equilibrium, the book is pulled down \(10 \mathrm{cm}\) and released. What is the period of oscillation? c. What is the book's maximum speed? At what position or positions does it have this speed?

A spring with spring constant \(15 \mathrm{N} / \mathrm{m}\) hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down \(6.0 \mathrm{cm}\) and released. If the ball makes 30 oscillations in \(20 \mathrm{s}\), what are its (a) mass and (b) maximum speed?

A mass on a string of unknown length oscillates as a pendulum with a period of 4.0 s. What is the period if a. The mass is doubled? b. The string length is doubled? c. The string length is halved? Parts a to d are independent questions, each referring to the initial situation.

I Astronauts on the first trip to Mars take along a pendulum that has a period on earth of 1.50 s. The period on Mars turns out to be \(2.45 \mathrm{s}\). What is the free-fall acceleration on Mars?

The amplitude of an oscillator decreases to \(36.8 \%\) of its initial value in \(10.0 \mathrm{s}\). What is the value of the time constant?

Calculate and draw an accurate position graph from \(t=0\) s to \(t=10 \mathrm{s}\) of a damped oscillator having a frequency of \(1.0 \mathrm{Hz}\) and a time constant of \(4.0 \mathrm{s}\).

An object in SHM oscillates with a period of 4.0 \(s\) and an amplitude of \(10 \mathrm{cm} .\) How long does the object take to move from \(x=0.0 \mathrm{cm}\) to \(x=6.0 \mathrm{cm} ?\)

A \(1.0 \mathrm{kg}\) block oscillates on a spring with spring constant 20 N/m. At \(t=0\) s the block is \(20 \mathrm{cm}\) to the right of the equilibrium position and moving to the left at a speed of \(100 \mathrm{cm} / \mathrm{s}\) Determine the period of oscillation and draw a graph of position versus time.

a. When the displacement of a mass on a spring is \(\frac{1}{2} A,\) 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?