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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