# Physics GRE Classical Mechanics-Oscillatory Motion

## Oscillatory Motion

### Problems

PGRE1777(3, 66, 90)
PGRE9677(8, 84, 92, 93)
PGRE9277(7, 61, 74)
PGRE8677(43, 60, 77)
PGRE0177(90)

### Formulas

#### Spring Constant

##### In Series

$$\frac{1}{k_t}=\frac{1}{k_1}+\frac{1}{k_2}$$

##### In Parallel

$$k_t=k_1+k_2$$

#### Period

$$T=\frac{1}{f}$$

$$T=\frac{2\pi}{\omega}$$

$$Time = \frac{Distance}{Angular Velocity}$$

#### Angular Frequency

$$\omega=\frac{2\pi}{T}$$

#### Period of Simple Pendulum

$$T=2\pi \sqrt{\frac{L}{g}}$$

#### Period of Spring Oscillation

$$T=2\pi\sqrt{\frac{m}{k}}$$

#### Displacement, Velocity and Acceleration

$$x=A\sin{\omega t}$$

$$v=\frac{dx}{dt}=A\omega \cos{\omega t}$$

$$a=\frac{dv}{dt}=-A\omega^2\sin{\omega t}=-\omega^2 x$$

#### Force

$$F=ma=m(-\omega^2 x)=-m\omega^2 x$$

Set $$m\omega^2=k$$

$$F=-kx$$

#### Damped Oscillation

$$F_d=-bv$$

#### Normal Mode

There are many questions related to normal mode in PGRE. We need to research them more.

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