SHM Teevra Series

Periodic Motion
It is the motion Which Repeats itself

after Fixed Interval of Time .
Ex: Rotation of earth, Revolution of earth

Periodic Motion
Time Period
Oscillatory Motion
It is the To & Fro motion about a Mean Position
(a) Motion of pendulum (b) To & fro motion of ball

Oscillatory Motion
All oscillatory motions are periodic, but All
Periodic Motions are not Oscillatory
Periodic Motion
Oscillatory Motion
SHM
It is a special case of oscillatory motion in which
Acceleration is always Directed Towards Mean Position
& is proportional to Displacement from M.P.
E.P. M.P. E.P.
x = A sin (𝜔t)
SHM
-ve MP A +ve
t=0 v
time =t
Equation of SHM
t=0
T/4
T/2
T A/2
T1 T2
-ve MP +ve
JEE Main 25th Jan 2023 S-2
A particle executes simple harmonic motion

between x = -A and x = +A. If time taken by
particle to go from x = 0 to A/2 is 2 s; then time
taken by particle in going from x = A/2 to A is
A 3s
B 2s
C 4s
D 1.5s
A particle executes simple harmonic motion

between x = -A and x = +A. If time taken by
particle to go from x = 0 to A/2 is 2 s; then time
taken by particle in going from x = A/2 to A is
A 3s
B 2s
C 4s
D 1.5s
Energy
T
U
X
JEE Main 13th April 2023 S-2
A particle executes SHM of amplitude A. The

distance from the mean position when it's
kinetic energy becomes equal to its potential
energy is :
A √2A
B 1/2 A
C 1/√2 A
D 2A
A particle executes SHM of amplitude A. The

distance from the mean position when it's
kinetic energy becomes equal to its potential
energy is :
A √2A
B 1/2 A
C 1/√2 A
D 2A
Remember!!!
Kinetic Energy oscillates with
double the frequency of
oscillation.
● fEnergy= 2 fSHM
MP
t=0 t=0
t=0
t=0
x = A sin ( ωt + Φ0)
Φ0= Initial Phase
MP
t=0 t=0
t=0
t=0
x = A sin ( ωt + Φ0)
Φ0= Initial Phase
Shifted SHM
Origin MP
t=0
A particle executes S.H.M. of amplitude A along

x-axis. At t = 0, the position of the particle is
x = A/2 and it moves along positives x-axis. The
displacement of particle in time t is
x = A sin(ωt + δ), then the value δ will be
A π/4
B π/2
C π/3
D π/6
A particle executes S.H.M. of amplitude A along

x-axis. At t = 0, the position of the particle is
x = A/2 and it moves along positives x-axis. The
displacement of particle in time t is
x = A sin(ωt + δ), then the value δ will be
A π/4
B π/2
C π/3
D π/6
Which graph represents the difference between

total energy and potential energy of a particle
executing SHM vs it's distance from mean
position?
A B
C D
Which graph represents the difference between

total energy and potential energy of a particle
executing SHM vs it's distance from mean
position?
A B
C D
The velocity of a particle executing SHM varies

with displacement (x) as 4v2 = 50 - x2 . The time
period of oscillations is x/7 s. The value of x
is_____.
The velocity of a particle executing SHM varies

with displacement (x) as 4v2 = 50 - x2 . The time
period of oscillations is x/7 s. The value of x
is_____.
Ans : 88
A block of mass M is placed on a platform which is
tied to a spring (K) as shown. The complete block +
platform assembly oscillates simple harmonically in
vertical direction. Find max amplitude such that
block doesn't leave platform.
A 𝜔2/g
M
B g/𝜔2
C 𝜔/g
D g/𝜔
M
A block of mass M is placed on a platform which is
tied to a spring (K) as shown. The complete block +
platform assembly oscillates simple harmonically in
vertical direction. Find max amplitude such that
block doesn't leave platform.
A 𝜔2/g
M
B g/𝜔2
C 𝜔/g
D g/𝜔
SHM of bodies in Equilibrium
● There should exist a point where net force on
particle is zero. This is called as mean position.
● A particle may or may not perform SHM about this
mean position.
SHM of bodies in Equilibrium
● To check, displace the particle slightly from its
mean position by distance x.
● If a net extra restoring force come into picture to
bring the particle back to its mean position, then
it will definitely perform SHM
Fnet = - kx
M
M
Hence A constant force only shifts M.P.
It does not impact time period of SHM.
a a
k k
M
A mass m is attached to two strings as shown in

figure. The spring constants of two springs are K1
and K2. For the frictionless surface, the time
period of oscillation of mass m is
D
A mass m is attached to two strings as shown in

figure. The spring constants of two springs are K1
and K2. For the frictionless surface, the time
period of oscillation of mass m is
D
M
1. Pulley and spring should be massless.
2. The coefficient of tension on the block
should be 1.
ni - coefficient of tension in the spring of

spring constant ki
M
M
M
m1 m2
l
a
C
Angular SHM
● There should exist a point where net torque on
particle is zero. This is called as mean position.
● A particle may or may not perform SHM about

this mean position.
Angular SHM
● To check, displace the particle slightly from its
mean position by angle 𝜃 .
● If a net extra restoring torque come into picture to
bring the particle back to its mean position, then it
will definitely perform SHM.
𝜏net ∝ 𝜃
𝜏net = - k𝜃
where I = MOI about axis of Rotation

Simple Pendulum
Simple Pendulum
● It is Independent of mass of bob.

Second’s Pendulum
● Its length is 1 m.
● Its Time period is 2 seconds.
● Time period is independent of mass of bob
SIMPLE PENDULUM
a
a
L
→a
Physical Pendulum
Hinge
● ℓ = distance of COM from

hinge point. l
CM
M,L

SHM Teevra Series

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Periodic Motion

It is the motion Which Repeats itself

Ex: Rotation of earth, Revolution of earth

(a) Motion of pendulum (b) To & fro motion of ball

A particle executes simple harmonic motion

A particle executes simple harmonic motion

A particle executes SHM of amplitude A. The

A particle executes SHM of amplitude A. The

A particle executes S.H.M. of amplitude A along

A particle executes S.H.M. of amplitude A along

Which graph represents the difference between

Which graph represents the difference between

The velocity of a particle executing SHM varies

The velocity of a particle executing SHM varies

A mass m is attached to two strings as shown in

A mass m is attached to two strings as shown in

ni - coefficient of tension in the spring of

● A particle may or may not perform SHM about

where I = MOI about axis of Rotation

● It is Independent of mass of bob.

● ℓ = distance of COM from

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