A mass attached to the end of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

A mass attached to the end of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have velocity equal to half its maximum velocity?

The molecule of carbon dioxide ($\ce{CO2}$) contains two polar covalent bonds. Why is the molecule nonpolar?

An oxygen atom at a particular site within a DNA molecule can be made to execute simple harmonic motion when illuminated by infrared light. The oxygen atom is bound with a spring-like chemical bond to a phosphorus atom, which is rigidly attached to the DNA backbone. The oscillation of the oxygen atom occurs with frequency $f=3.7 \times 10^{13} \mathrm{~Hz}$. If the oxygen atom at this site is chemically replaced with a sulfur atom, the spring constant of the bond is unchanged (sulfur is just below oxygen in the Periodic Table). Predict the frequency after the sulfur substitution.

An object with mass $2.7 \mathrm{~kg}$ is executing simple harmonic motion, attached to a spring with spring constant $k=310 \mathrm{~N} / \mathrm{m}$. When the object is $0.020 \mathrm{~m}$ from its equilibrium position, it is moving with a speed of $0.55 \mathrm{~m} / \mathrm{s}$. Calculate the maximum speed attained by the object.

An object with mass $2.7 \mathrm{~kg}$ is executing simple harmonic motion, attached to a spring with spring constant $k=310 \mathrm{~N} / \mathrm{m}$. When the object is $0.020 \mathrm{~m}$ from its equilibrium position, it is moving with a speed of $0.60 \mathrm{~m} / \mathrm{s}$. Calculate the amplitude of the motion.

An object with mass $2.7 \mathrm{~kg}$ is executing simple harmonic motion, attached to a spring with spring constant $k=310 \mathrm{~N} / \mathrm{m}$. When the object is $0.020 \mathrm{~m}$ from its equilibrium position, it is moving with a speed of $0.55 \mathrm{~m} / \mathrm{s}$. Calculate the amplitude of the motion.

An object with mass $2.7 \mathrm{~kg}$ is executing simple harmonic motion, attached to a spring with spring constant $~k=280 \mathrm{~N} / \mathrm{m}.~$ When the object is $0.020 \mathrm{~m}$ from its equilibrium position, $~$it is moving with a speed of $~0.55 \mathrm{~m} / \mathrm{s}.~$Calculate the amplitude of the motion.

(II) At t=0, a 785-g mass at rest on the end of a horizontal spring (k=184 N/m) is struck by a hammer which gives it an initial speed of 2.26 m/s. Determine the position as a function of time.

If one oscillation has $~5.0~$ times the energy of a second one of equal frequency and mass, what is the ratio of their amplitudes?

The position of a $\mathrm{SHO}$ as a function of time is given by $x=3.8 \cos (5 \pi t / 4+\pi / 6)$ where $t$ is in seconds and $x$ in meters. Find the velocity and acceleration at $t=2.5 \mathrm{~s}$.

A uniform meter stick of mass $M$ is pivoted on a hinge at one end and held horizontal by a spring with spring constant $~k~$ attached at the other end see the fig. If the stick oscillates up and down slightly, what is its frequency? [Hint: Write a torque equation about the hinge.]

The position of a SHO as a function of time is given by $x=3.8 \cos (5 \pi t / 4+\pi / 6)$ where $~t~$ is in seconds and $~x~$ in meters. Find the velocity and acceleration at $~t=2.0\mathrm{~s}$.

The position of a $\mathrm{SHO}$ as a function of time is given by $x=3.8 \cos (5 \pi t / 4+\pi / 6)$ where $t$ is in seconds and $x$ in meters. Find the position and velocity at $t=0$