Chapter 15: Oscillations

An object in simple harmonic motion has amplitude $4.0cm$and frequency $4.0Hz$, and at $t=0s$it passes through the equilibrium point moving to the right. Write the function$x\left(t\right)$ that describes the object’s position

An object in simple harmonic motion has amplitude $4.0cm$and frequency $4.0Hz$, and at $t=0s$it passes through the equilibrium point moving to the right. Write the function $x\left(t\right)$that describes the object’s position.

What is the difference between the driving frequency and the natural frequency of an oscillator?

An object in simple harmonic motion has amplitude $8.0cm$and frequency$0.50Hz$. At $t=0s$it has its most negative position. Write the function $x\left(t\right)$that describes the object’s position.

An air-track glider attached to a spring oscillates with a period of $1.5s$. At $t=0s$the glider is $5.00cm$left of the equilibrium position and moving to the right at $36.3cm/s$.

a. What is the phase constant?

b. What is the phase at $t=0s$, $0.5s$, $1.0s$, and $1.5s$?

A block attached to a spring with unknown spring constant oscillates with a period of $2.0s$.What is the period if

a. The mass is doubled?

b. The mass is halved?

c. The amplitude is doubled?

d. The spring constant is doubled? Parts a to d are independent questions, each referring to the initial situation.

A $200g$air-track glider is attached to a spring. The glider is pushed in 10 cm .and released. A student with a stopwatch finds that $10$oscillations take 12.0 s . What is the spring constant?

A $200\mathrm{g}$mass attached to a horizontal spring oscillates at a frequency of $2.0\mathrm{Hz}$. At $t=0\mathrm{s}$, the mass is at $x=5.0\mathrm{cm}$and has $v_x=-30\mathrm{cm}/\mathrm{s}$. Determine:

$a.$The period.

$b.$The angular frequency.

$c.$The amplitude.

$d.$The phase constant.

$e.$The maximum speed.

$f.$The maximum acceleration.

$g.$The total energy.

$h.$The position at $t=0.40\mathrm{s}$.

The position of a $50g$oscillating mass is given by $x\left(t\right)=\left(2.0cm\right)\cos \left(10t-\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right)$, where $t$is in $s$. Determine:

a. The amplitude.

b. The period.

c. The spring constant.

d. The phase constant.

e. The initial conditions.

f. The maximum speed.

g. The total energy.

h. The velocity at $t=0.40s$.

A $1.0kg$block is attached to a spring with spring constant $16N/m$. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives its a speed of $40cm/s$.

What are

a. The amplitude of the subsequent oscillations?

b. The block's speed at the point where $x=\frac{1}{2}A$?