Question 1

A block of mass $$m$$ slides with initial velocity $$v_i on a $$frictionless surface and compresses a spring with spring constant $$k$$ until it comes to rest. What is the maximum compression $$x_{max} of $$the spring?

Accepted Answer

$$x_{max} = \sqrt{\frac{1}{2} \frac{mv_i^2$}{k}}$$

Question 2

Which parameter in the general wave equation $$y(x,t) = A \sin\left(2\pi \frac{x}{\lambda} \pm 2\pi \frac{t}{T} + \phi \right)$$ determines the direction the wave is traveling?

Accepted Answer

The plus/minus sign in front of the time variable

Question 3

A mass-spring system and a simple pendulum both have a period of $$1.50 s on $$Earth. If you take them to another planet with unknown gravity, which device can you use to determine the gravitational acceleration $$g on $$that planet?

Accepted Answer

Only the pendulum

Question 4

If the amplitude of a mass-spring system is doubled, what happens to the maximum velocity and the period?

Accepted Answer

The maximum velocity will double while the period remains the same.

Question 5

Which of the following best describes a transverse wave?

Accepted Answer

The displacement is perpendicular to the direction of wave travel.

Question 6

The total mechanical energy $$E_{tot} of a $$mass-spring system is given by:

Accepted Answer

$$E_{tot} = \frac{1}{2}mv^2$ + \frac{1}{2}kx^2$

Question 7

A wave on a string has a wavelength $$\lambda = 2 m $$and a frequency $$f = 5 Hz. $$What is the speed of the wave?

Accepted Answer

$$v = 10 m/s$$

Question 8

At the equilibrium position ($$x = 0) of a $$mass-spring system, which statement is true?

Accepted Answer

The kinetic energy is maximum and the potential energy is zero.

Question 9

Which equation correctly gives the period of a simple pendulum of length $$L in a $$gravitational field $$g$$?

Accepted Answer

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Question 10

A longitudinal wave is characterized by:

Accepted Answer

Displacement parallel to the direction of wave travel.

Question 11

The wave function $$y(x,t) = A \sin(kx - \omega t + \phi)$$ describes a wave traveling:

Accepted Answer

In the $$+x$$ direction

Question 12

The spring force is given by:

Accepted Answer

$$F_{spring} = -k \Delta x$$

Question 13

If a wave has a period $$T = 0.2 s$$, what is its frequency?

Accepted Answer

$$f = 5 Hz$$

Question 14

Which of the following is true about the energy in a mass-spring system at the turning points ($$x = \pm A$$)?

Accepted Answer

All energy is potential.

Question 15

The angular frequency $$\omega of a $$mass-spring system is:

Accepted Answer

$$\omega = 2\pi f$$

Question 16

A wave has a displacement described by $$y(x,t) = A \sin(kx + \omega t). $$What is the direction of propagation?

Accepted Answer

Negative $$x$$ direction

Question 17

The speed of a wave on a string under tension $$F_T$$ and with mass per unit length $$\mu is$$:

Accepted Answer

$$v = \sqrt{\frac{F_T}{\mu}}$$

Question 18

Which of the following is NOT a property of periodic waves?

Accepted Answer

Their amplitude determines their speed.

Question 19

The phase difference $$\Delta \phi$$ between two points separated by $$\Delta x on a $$wave with wavelength $$\lambda is$$:

Accepted Answer

$$\Delta \phi = 2\pi \frac{\Delta x}{\lambda}$$

Conservation of Energy in Simple Harmonic Motion and Introduction to Waves

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