Q: A violin string playing the note A oscillates at 440 Hz. What is the period of oscillation of the string?

$$2.27 \times 10$$^{-3}$$\ \mathrm{s}$$

Q: The vibration frequency of a hydrogen chloride molecule is $$8.66 \times 10$$^{13}$$\ \mathrm{Hz}. $$How long does it take the molecule to complete one oscillation?

$$1.15 \times 10$$^{-14}$$\ \mathrm{s}$$

Question 1

A violin string playing the note A oscillates at 440 Hz. What is the period of oscillation of the string?

Accepted Answer

$$2.27 	imes 10$$^{-3}$$\ \mathrm{s}$$

Question 2

The vibration frequency of a hydrogen chloride molecule is $$8.66 	imes 10$$^{13}$$\ \mathrm{Hz}. $$How long does it take the molecule to complete one oscillation?

Accepted Answer

$$1.15 	imes 10$$^{-14}$$\ \mathrm{s}$$

Question 3

Which of the following equations describes simple harmonic motion?

Accepted Answer

$$x = 5 \sin 23t$$

Question 4

A 12.0-N object oscillates in simple harmonic motion at the end of an ideal vertical spring. Its position is $$y(t) = 4.50\ \mathrm{cm} \cos[(19.5\ \mathrm{s}^{-1})t - \pi/8]. $$What is the spring constant of the spring?

Accepted Answer

$$k = 231\ \mathrm{N/m}$$

Question 5

A 2.25-kg object is attached to a horizontal ideal massless spring on a frictionless table. What should be the spring constant $$k so $$that the maximum acceleration of the object will be $$g$$ when it oscillates with amplitude $$A = 4.50\ \mathrm{cm}$$?

Accepted Answer

$$k = 490\ \mathrm{N/m}$$

Question 6

A 1.6-kg block on a horizontal frictionless surface is attached to an ideal massless spring with $$k = 190\ \mathrm{N/m}. $$The block is pulled to $$x = +0.080\ \mathrm{m}$$ and released from rest. What is the velocity of the block at $$t = 0.40\ \mathrm{s}$$?

Accepted Answer

$$-0.30\ \mathrm{m/s}$$

Question 7

A simple pendulum on Earth has a period of $$1.75\ \mathrm{s}. On $$Planet X, its period is $$2.14\ \mathrm{s}. $$What is the acceleration due to gravity on Planet X?

Accepted Answer

$$g_X = 7.0\ \mathrm{m/s}^2$$

Question 8

The angle that a swinging simple pendulum makes with the vertical is $$\Theta(t) = (0.150\ \mathrm{rad}) \cos[(2.85\ \mathrm{rad/s})t + 1.66]. $$What is the length of the pendulum?

Accepted Answer

$$0.83\ \mathrm{m}$$

Question 9

A $$0.25\ \mathrm{kg}$$ ideal harmonic oscillator has a total mechanical energy of $$4.00\ \mathrm{J}. If $$the oscillation amplitude is $$20.0\ \mathrm{cm}$$, what is the oscillation frequency?

Accepted Answer

$$2.3\ \mathrm{Hz}$$

Question 10

A $$0.50\ \mathrm{kg}$$ object is attached to an ideal massless spring of spring constant $$20\ \mathrm{N/m} on a $$frictionless surface. The object oscillates in simple harmonic motion and has a speed of $$1.5\ \mathrm{m/s} at $$the equilibrium position. What is the amplitude of vibration?

Accepted Answer

$$0.24\ \mathrm{m}$$

Question 11

A $$1.5\ \mathrm{kg}$$ mass attached to a spring with $$k = 20.0\ \mathrm{N/m}$$ oscillates on a frictionless track. Released from rest at $$x = 10.0\ \mathrm{cm}$$, what is the maximum speed of the mass?

Accepted Answer

$$0.36\ \mathrm{m/s}$$

Question 12

A $$6.8\ \mathrm{kg}$$ object is attached to a spring with $$k = 1690\ \mathrm{N/m}. $$What is the maximum speed the object reaches during its motion if the amplitude is $$0.10\ \mathrm{m}$$?

Accepted Answer

$$1.57\ \mathrm{m/s}$$

Question 13

An object weighing $$44.1\ \mathrm{N}$$ hangs from a vertical massless ideal spring. When set in vertical motion, the object obeys $$y(t) = (6.20\ \mathrm{cm}) \cos[(2.74\ \mathrm{rad/s})t - 1.40]. $$What is the period of oscillation?

Accepted Answer

$$2.29\ \mathrm{s}$$

Question 14

A $$2.450\ \mathrm{N}$$ object is attached to an ideal massless spring and undergoes simple harmonic oscillations with a period of $$0.640\ \mathrm{s}. $$What is the spring constant of the spring?

Accepted Answer

$$24.1\ \mathrm{N/m}$$

Question 15

A building in San Francisco has light fixtures consisting of small $$2.35\ \mathrm{kg}$$ bulbs with shades hanging from the ceiling at the end of light, thin cords $$1.50\ \mathrm{m}$$ long. If a minor earthquake occurs, how many swings per second will these fixtures make?

Accepted Answer

$$0.41\ \mathrm{Hz}$$

Question 16

The position of an object oscillating on an ideal spring is $$x = (12.3\ \mathrm{cm}) \cos[(1.26\ \mathrm{s}^{-1})t]. $$What is the magnitude of the acceleration at $$t = 0.815\ \mathrm{s}$$?

Accepted Answer

$$0.19\ \mathrm{m/s}^2$$

Question 17

The $$x-$$component of the velocity of an object vibrating along the $$x-$$axis is $$v_x(t) = (0.445\ \mathrm{m/s}) \sin[(25.4\ \mathrm{rad/s})t + 0.223]. $$What is the amplitude of the motion?

Accepted Answer

$$0.0175\ \mathrm{m}$$

Question 18

A $$1.5\ \mathrm{kg}$$ mass attached to a spring with $$k = 20.0\ \mathrm{N/m}$$ oscillates on a frictionless track. What is the total energy of the oscillating system if the amplitude is $$0.10\ \mathrm{m}$$?

Accepted Answer

$$0.20\ \mathrm{J}$$

Question 19

An object weighing $$44.1\ \mathrm{N}$$ hangs from a vertical massless ideal spring. When set in vertical motion, the object obeys $$y(t) = (6.20\ \mathrm{cm}) \cos[(2.74\ \mathrm{rad/s})t - 1.40]. $$What is the spring constant of the spring?

Accepted Answer

$$5.89\ \mathrm{N/m}$$

Exam Review Guidance: Oscillatory Motion, Simple Harmonic Motion, Springs, Pendulums, and Energy

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