A $12.5 \mathrm{~g}$ clothesline is stretched with a tension of $22.1 \mathrm{~N}$ between two poles $7.66 \mathrm{~m}$ apart. What is the frequency of the fundamental harmonic?

A hula hoop hangs from a peg. Find the period of the hoop as it gently rocks back and forth on the peg. (For a hoop with axis at the rim $I=2 m R^2$, where $R$ is the radius of the hoop.)

A simple pendulum of length 2.5 m makes 5.0 complete swings in 16 s. What is the acceleration due to gravity at the location of the pendulum?

An astronaut uses a Body Mass Measurement Device to measure her mass. If the force constant of the spring is $2700 \mathrm{~N} / \mathrm{m}$, her mass is $75 \mathrm{~kg}$, and the amplitude of her oscillation is $1.9 \mathrm{~cm}$, what is her maximum speed during the measurement?

A $1.6-\mathrm{kg}$ mass attached to a spring oscillates with an amplitude of $7.3 \mathrm{~cm}$ and a frequency of $2.8 \mathrm{~Hz}$. What is its energy of motion?

A 1.5 kg mass attached to a spring and oscillates with an amplitude of 9.3 cm and a frequency of 5.8 Hz. What is the energy of its motion?

A $0.285-\mathrm{kg}$ mass is attached to a spring with a force constant of $53.4 \mathrm{~N} / \mathrm{m}$. If the mass is displaced $0.180 \mathrm{~m}$ from equilibrium and released, what is its speed when it is $0.135 \mathrm{~m}$ from equilibrium?

System $A$ consists of a mass $m$ attached to a spring with a force constant $k$; system $B$ has a mass $2 m$ attached to a spring with a force constant $k$; system $\mathrm{C}$ has a mass $3 \mathrm{~m}$ attached to a spring with a force constant $6 k$; and system $D$ has a mass $m$ attached to a spring with a force constant $4 k$. Rank these systems in order of increasing period of oscillation.

The pistons in an internal combustion engine undergo a motion that is approximately simple harmonic. If the amplitude of motion is $3.5 \mathrm{~cm}$, and the engine runs at $1700 \mathrm{rev} / \mathrm{min}$, find the maximum speed of the pistons.

The pistons in an internal combustion engine undergo a motion that is approximately simple harmonic. If the amplitude of motion is $3.5 \mathrm{~cm}$, and the engine runs at $1700 \mathrm{rev} / \mathrm{min}$, find the maximum acceleration of the pistons.

An object executing simple harmonic motion has a maximum speed of $4.1 \mathrm{~m} / \mathrm{s}$ and a maximum acceleration of $0.85 \mathrm{~m} / \mathrm{s}^2$. Determine (a) the amplitude and (b) the period of this motion.

An object executing simple harmonic motion has a maximum speed of $4.1 \mathrm{~m} / \mathrm{s}$ and a maximum acceleration of $0.85 \mathrm{~m} / \mathrm{s}^2$. Determine the period of this motion.

A child rocks back and forth on a porch swing with an amplitude of $0.204 \mathrm{~m}$ and a period of $2.80 \mathrm{~s}$. Assuming the motion is approximately simple harmonic, find the child's maximum speed.

A ball rolls on a circular track of radius $0.62 \mathrm{~m}$ with a constant angular speed of $1.3 \mathrm{rad} / \mathrm{s}$ in the counterclockwise direction. If the angular position of the ball at $t=0$ is $\theta=0$, find the $x$ component of the ball's position at the times $2.5 \mathrm{~s}, 5.0 \mathrm{~s}$, and $7.5 \mathrm{~s}$. Let $\theta=0$ correspond to the positive $x$ direction.