Oscillations

$\dfrac{d^{2}x}{dt^{2}}=-\omega^{2}x$

$\dfrac{d^{2}x}{dt^{2}}=-\omega^{2}t$

$\dfrac{d^{2}x}{dt^{2}}=-\omega\sqrt{t}$

$\dfrac{d^{2}x}{dt^{2}}=-\omega\sqrt{x}$

zero

A

2A

4A

periodic and simple harmonic

non- periodic

periodic but not simple harmonic

non periodic but simple harmonic

reduce the amplitude of oscillation.

reduce the mass of the bob.

reduce the length of pendulum.

increase the length of pendulum.

restoring force per unit mass

restoring force per unit displacement

restoring force per unit mass per unit displacement

acceleration per unit mass per unit displacement

free vibration

damped harmonic oscillator

forced oscillator

resonant oscillator

When v is maximum, a is zero

When v is maximum, a is maximum

Value of a is zero, whatever may be the value of v

When v is zero, a is zero

zero

$\dfrac{A\omega}{2}$

$A\omega$

$\dfrac{A\omega^{2}}{2}$

both speed and magnitude acceleration are zero

both speed and magnitude acceleration are maximum

speed is maximum but magnitude acceleration is zero

speed is zero but magnitude acceleration is maximum

the motion is periodic.

its acceleration is directed towards a fixed point in its path.

the magnitude of acceleration is directly proportional to displacement.

the acceleration is directed in the direction of displacement.

$x$-axis only

$y$-axis only

reference circle

any diameter of reference circle

$0.2 \pi \mathrm{~s}$

$0.4 \pi \mathrm{~s}$

$0.6 \pi \mathrm{~s}$

$0.8 \pi \mathrm{~s}$

$\pi \mathrm{rad}$

$\dfrac{\pi}{2} \mathrm{rad}$

$\dfrac{\pi}{4} \mathrm{rad}$

0 rad

$F=A\cos(Ky)$

$F=A\sin(Ky)$

$F=-AKy$

$F=AKy$