Oscillations

What are oscillations

Periodic to-and-fro motions of a body about its mean (or equilibrium) position

What is a time period (for pendulums and NOT for circles;defination)

It is the amount of time required by the body to complete 1 oscillation

What is a time period (for circles and NOT for pendulums)

It is the amount of time required by the body to complete 1 revolution

What is the formula for angular frequency, and what are its units?

k/m
were,

k → Stiffness of the spring (From Hooke’s law)

m→ mass

What is the formula for finding out the time of oscillation

t = (T/2⊼)*ʘ

How can you write pi in time period’s terms?

T/2 = ⊼

When a particle is moving clockwise and anticlockwise, what happens to its angle?

• Anticlockwise :- +ve

• Clockwise :- -ve

What is the formula for the relation between velociy and distance in SHM?

V = w * √A²-x²

where,

w → Angular velocity

A → Amplitude

x → Distance

What is the formula for acceleration (w.r.t. position for SHM)?

a = -w²x

What is a second’s pendulum

It is a pendulum whose length is 1 meter and has a time period of 2 sec

What is the formula for the time period if the simple pendulum is very large compared to the radius of the Earth; What is it’s value?

It’s value is 84.6 minutes

What is the changes in cos and sin as you change the phase between them by ⊼/2

• cos⁡(θ+π/2)= −sin⁡(θ)

• sin⁡(θ+π/2)= cos⁡(θ)

What is the formula that will be used to find the time period when the friction of the surface is sufficient to cause a body to roll when it is attached to a string

What is the formula that we will use when damping is occurring in oscillations?

k = b/2m

where,

where:

• b: damping constant

• m: mass

• k: the damping coefficient (not the same as decay constant in general exponential decay)

  • If k is big → fast decay 😱

  • If k is small → slow decay 🐢

What is the formula that we will use to represent exponential decay?

A_t = A e^-kt
Where:

• A(t): Amount left after time t

• A₀: Initial amount (at time 0)

• k: decay constant (positive value)

• t: time

• e: Euler's number (~2.718)

What is the formula we will use for length when the distance of the object > radius of the earth?