A $0.40-\mathrm{kg}$ object is attached to a spring with force constant $160 \mathrm{~N} / \mathrm{m}$ so that the object is allowed to move on a horizontal frictionless surface. The object is released from rest when the spring is compressed $0.15 \mathrm{~m}$. Find (a) the force on the object and

"A $5.00\text{-kg}$ object on a frictionless horizontal surface is attached to one end of a horizontal spring that has a force constant $k=700 \text{~N/m}$. The spring is stretched $8.00 \text{~cm}$ from equilibrium and released. What are $(b)$ the period, "

The frequency of vibration of an object-spring system is $5.00 \mathrm{~Hz}$ when a $4.00-\mathrm{g}$ mass is attached to the spring. What is the force constant of the spring?

A $2.4\text{-kg}$ object on a frictionless horizontal surface is attached to the end of a horizontal spring that has a force constant $k=4.5 \text{kN/m}$. The spring is stretched $10 \text{~cm}$ from equilibrium and released. What are $(a)$ the frequency of the motion,

A gun fires a bullet vertically into a $1.40\text {-kg}$ block of wood at rest on a thin horizontal sheet. If the bullet has a mass of $15.0 \text {~g}$ and a speed of $230 \text {~m/s}$, how high will the block rise into the air after the bullet becomes embedded in it?

A child in a boat throws a 6.40-kg package out horizontally with a speed of 10.0 m/s. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance.

A $3.0-\mathrm{kg}$ ball of clay with a speed of $21 \mathrm{~m} / \mathrm{s}$ is thrown against a wall and sticks to the wall. What is the magnitude of the impulse exerted on the ball?

Two particles oscillate in simple harmonic motion along a common straight-line segment of length A. Each particle has a period of 1.5 s, but they differ in phase by

$$\pi / 6 \text { rad }$$

. (a) How far apart are they (in terms of A) 0.60 s after the lagging particle leaves one end of the path? (b) Are they then moving in the same direction, toward each other, or away from each other?

Two particles oscillate in simple harmonic motion along a common straight-line segment of length A. Each particle has a period of 1.5 seconds, but they differ in phase by $\pi/6 \text{~rad}$. How far apart are they (in terms of A) 0.50 seconds after the lagging particle leaves one end of the path?

Two particles oscillate in simple harmonic motion along a common straight-line segment of length A. Each particle has a period of 1.5 seconds, but they differ in phase by $\pi/6 \text{~rad}$. Are they then moving in the same direction, toward each other, or away from each other?

Given that a ball is dropped from a height of $4.00 \mathrm{~m}$ makes an elastic collision with the ground. Assuming that no mechanical energy is lost due to air resistance, find the period of the motion.

Given that a ball is dropped from a height of $4.00 \mathrm{~m}$ makes an elastic collision with the ground. Assuming that no mechanical energy is lost due to air resistance, is the motion simple harmonic? Explain.

The position of a particle is given by the expression $\mathrm{M} x=4.00 \cos (3.00 \pi t+\pi)$, where $x$ is in meters and $t$ is in seconds. Determine
(b) period of the motion,

The position of a particle is given by the expression

$$x=4.00 \cos (3.00 \pi t+\pi),$$

where x is in meters and t is in seconds. Determine (a) the frequency and (b) period of the motion, (c) the amplitude of the motion, (d) the phase constant, and (e) the position of the particle at t = 0.250 s.