SHM formulas

Every formula JEE Advanced expects you to know for SHM, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

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Formulas: 32
Subject: Physics
Exam: JEE Advanced
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SHM, every formula

32 formulas, typeset and free. Print it, or keep it open beside your practice.

SHM restoring force
$F = - k x$
General equation of SHM
$x = A sin (ω t + ϕ)$
Angular frequency
$ω = \frac{2 π}{T} = 2 π f$
Velocity in SHM
$v = ω A^{2} - x^{2}$
Maximum velocity
$v_{m a x} = ω A$
Acceleration in SHM
$a = - ω^{2} x$
Maximum acceleration
$a_{m a x} = ω^{2} A$
Kinetic energy
$K = \frac{1}{2} m ω^{2} (A^{2} - x^{2})$
Potential energy
$U = \frac{1}{2} k x^{2} = \frac{1}{2} m ω^{2} x^{2}$
Total energy
$E = \frac{1}{2} m ω^{2} A^{2} = \frac{1}{2} k A^{2}$
Spring–mass period
$T = 2 π \frac{m}{k}$
Angular frequency (spring)
$ω = \frac{k}{m}$
Two-mass spring period
$T = 2 π \frac{μ}{k}$
μ = reduced mass
Springs in series
$\frac{1}{k _{e q}} = \frac{1}{k _{1}} + \frac{1}{k _{2}}$
Springs in parallel
$k_{e q} = k_{1} + k_{2}$
Simple pendulum period
$T = 2 π \frac{l}{g}$
Second's pendulum
$T = 2 s, l \approx 1 m$
Physical (compound) pendulum
$T = 2 π \frac{I}{m g l}$
Torsional pendulum
$T = 2 π \frac{I}{C}$
C = torsional constant
Conical pendulum period
$T = 2 π \frac{h}{g}$
Pendulum in a lift (up)
$T = 2 π \frac{l}{g + a}$
Pendulum in a lift (down)
$T = 2 π \frac{l}{g - a}$
Effective g (horizontal a)
$g_{e f f} = g^{2} + a^{2}$
Average KE over a cycle
$⟨ K ⟩ = \frac{1}{4} k A^{2}$
Average PE over a cycle
$⟨ U ⟩ = \frac{1}{4} k A^{2}$
Frequency of energy
$f_{e n er g y} = 2 f_{d i s pl a ce m e n t}$
Superposition amplitude
$A = A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos θ$
Damping force
$F = - b v$
Damped amplitude
$A = A_{0} e^{- b t /2 m}$
Damped energy
$E (t) = \frac{1}{2} k A_{0}^{2} e^{- b t / m}$
Critical damping
$b^{2} = 4 mk$
Resonance amplitude
$A = \frac{F _{0}}{ω _{d} b}$
at resonance

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SHM formulas

SHM, every formula

SHM restoring force

General equation of SHM

Angular frequency

Velocity in SHM

Maximum velocity

Acceleration in SHM

Maximum acceleration

Kinetic energy

Potential energy

Total energy

Spring–mass period

Angular frequency (spring)

Two-mass spring period

Springs in series

Springs in parallel

Simple pendulum period

Second's pendulum

Physical (compound) pendulum

Torsional pendulum

Conical pendulum period

Pendulum in a lift (up)

Pendulum in a lift (down)

Effective g (horizontal a)

Average KE over a cycle

Average PE over a cycle

Frequency of energy

Superposition amplitude

Damping force

Damped amplitude

Damped energy

Critical damping

Resonance amplitude

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