A $175$-$\mathrm{g}$ glider on a horizontal, frictionless air track is attached to a fixed ideal spring with force constant $155 \mathrm{~N} / \mathrm{m}$. At the instant you make measurements on the glider, it is moving at $0.815$ m$/$s and is $3.00$ cm from its equilibrium point. Use $\it{energy}$ $\it{conservation}$ to find
($c$) What is the angular frequency of the oscillations?

A 0.150-kg glider is moving to the right with a speed of 0.80 m/s on a frictionless, horizontal air track. The glider has a head-on collision with a 0.300-kg glider that is moving to the left with a speed of 2.20 m/s. Find the final velocity (magnitude and direction) of each glider if the collision is elastic.

A $0.500$-$\mathrm{kg}$ glider, attached to the end of an ideal spring with force constant $k=450 \mathrm{~N} / \mathrm{m}$, undergoes SHM with an amplitude of $0.040$ m. Compute
(e) the total mechanical energy of the glider at any point in its motion.

A proud deep-sea fisherman hangs a $65.0$-$\mathrm{kg}$ fish from an ideal spring having negligible mass. The fish stretches the spring $0.180$ m.
(b) What is the period of oscillation of the fish?

A proud deep-sea fisherman hangs a $65.0$-$\mathrm{kg}$ fish from an ideal spring having negligible mass. The fish stretches the spring $0.180$ m.
($c$) What is the maximum speed it will reach?

You pull a simple pendulum $0.240$ m long to the side through an angle of $3.50$ $\degree$ and release it.
(b) How much time does it take if the pendulum is released at an angle of $1.75$ $\degree$ instead of $3.50$ $\degree$?

You pull a simple pendulum 0.240 m long to the side through an angle of $3.50 ^ { \circ }$ and release it. (a) How much time does it take the pendulum bob to reach its highest speed? (b) How much time does it take if the pendulum is released at an angle of $1.75 ^ { \circ }$ instead of $3.50 ^ { \circ }$?

A proud deep-sea fisherman hangs a 65.0-kg fish from an ideal spring having negligible mass. The fish stretches the spring 0.180 m. (a) Find the force constant of the spring. The fish is now pulled down 5.00 cm and released. (b) What is the period of oscillation of the fish? (c) What is the maximum speed it will reach?

A $0.500$-$\mathrm{kg}$ glider, attached to the end of an ideal spring with force constant $k=450 \mathrm{~N} / \mathrm{m}$, undergoes SHM with an amplitude of $0.040$ m. Compute
(d) the acceleration of the glider at $x=-0.015 \mathrm{~m}$;

A $0.500$-$\mathrm{kg}$ glider, attached to the end of an ideal spring with force constant $k=450 \mathrm{~N} / \mathrm{m}$, undergoes SHM with an amplitude of $0.040$ m. Compute
($c$) the magnitude of the maximum acceleration of the glider;

A $0.500$-$\mathrm{kg}$ glider, attached to the end of an ideal spring with force constant $k=450 \mathrm{~N} / \mathrm{m}$, undergoes SHM with an amplitude of $0.040$ m. Compute
(b) the speed of the glider when it is at $x=-0.015$ m;

A 1.50-kg mass on a spring has displacement as a function of time given by

$$x ( t ) = ( 7.40 \mathrm { cm } ) \cos [ ( 4.16 \mathrm { rad } / \mathrm { s } ) \mathrm { t } - 2.42 ]$$

Find:

(a) the time for one complete vibration;

(b) the force constant of the spring;

(c) the maximum speed of the mass;

(d) the maximum force on the mass;

(e) the position, speed, and acceleration of the mass at t = 1.00 s;

(f) the force on the mass at that time.

A $0.500$-$\mathrm{kg}$ mass on a spring has velocity as a function of time given by $v_x(t)=-(3.60 \mathrm{~cm} / \mathrm{s}) \sin [(4.71 \mathrm{rad} / \mathrm{s}) t-(\pi / 2)]$. What are
($c$) the maximum accel- eration of the mass;

A $0.500$-$\mathrm{kg}$ mass on a spring has velocity as a function of time given by $v_x(t)=-(3.60 \mathrm{~cm} / \mathrm{s}) \sin [(4.71 \mathrm{rad} / \mathrm{s}) t-(\pi / 2)]$. What are
(d) the force constant of the spring?