shm

Restoring force characteristics

Restoring force is max when displacement is max

Restoring force on the mass always acts towards the equilibrium position

Characteristics of a particles acceleration

Acceleration of a particle is least when speed of it is greatest at equilibrium position

Acceleration is always opposite direction to its displacement

What is the phase difference between a displacement-time and velocity time graph

Pi/2

What is the phase difference between a displacement-time and acceleration-time graph

Pi

Equation for displacement

X=Asinwt

A is the amplitude

Equation for velocity and velocity max

V=+- w square root (A²-x²)

V max=wA

Equation for acceleration and acceleration max

a=-w²x

a=-w²A

How do you calculate the amplitude and time period by just a length of string pulled and the time it take to get back to the equilibrium position

Amplitude is the length the string is pulled

To find time period:

1. How many time the amplitude will make one full wavelength. So 1/n cycle

2. T=time it take to get back to equilibrium position x n

Definition for SHM

Acceleration/restoring force is directly proportional from the equilibrium position and directed towards it

How to find the no. Of oscillations when two 2 pendulums with two different time periods are equal

The pendulum with the smaller time period most likely will have at least one more oscillation that the pendulum with the larger time period

Greater time period x n = (n+1) x lesser timer period

Hooke’s law

F=kx

Equation for time period in a pendulum and general time period equation

T= 2pi x square root (length/gfs)

T=1/f

Equation for time period for a mass spring

2pi x square root (mass/spring constant)

How to find max kinetic energy for a wave

V max=wA

½ m(wA)²

E total=

½ kA²

Where k= spring constant

How to find an original length on a pendulum before it was increased by n length when the time period doubled

T=2pi x square root (L/g)

T is directly proportional to the square root length

2T=2 square root L=square root 4L

L+n=4L

L=n/3

Definition for damping

Reduction in amplitude of oscillations over time due to the presence of a dissipative force

What happens to the amplitude when it is damped

oscillation decays exponentially

Equation for amplitude when it is dampened

An=A0/2n

Where A0 is the initial amplitude

And n is the no. Of damping

Increase in damping means

Less curve at all frequencies

Less energy produced

Amplifying resonant frequency decreases

Resonant peaks are broader

Resonant frequency is lower

Definition of light damping

Oscillation with steadily decreasing amplitude

Definition of critical damping

System returns to equilibrium position in the shortest time possible

definition of heavy damping

System returns to equilibrium position when it is displaced and released but will happen slower than critical damping

Definition for resonance

When the driving frequency matches the natural frequency of the oscillator, max energy is transferred and therefore amplitude is max