Oscillations
SHORT NOTES
Simple Harmonic Motion
F=-kx T V&
(in accelerating Reference Frame): gor is net
General equation of S.H.M. is x = A sin (ot + ): (ot + ) is phase acceleration due to pseudo force and gravitational force.
of the motion and is initial phase of the motion.
Time period of simple pendulum in Accelerating lift.
(i) If velocity of lift in constant,
T = 2rf
&efr8
Time period (T): T=
=2k
m
T-24 (.: a = 0)
(i) Iflif is moving upwards with acceleration a Br=8ta
Speed: v = aa
T=27
Acceleration: a = -o'x Vg+a
(iü) Iflift is moving downwards with acceleration a,
Kinetie Eaergy (KEN =mm (#-)-(4-+) Ber g-a
T-2 Vg-a
Potential Enegy (PE): kr=ma (iv) Iflift falls downwards freely,
Ber=0
Total Mechanical Energy (TME) T=0
= constant Compound Pendulum/Physical Pendulum
Spring-Mass System
Time Period (): T= 2r mgl
where, I = t ml'; lis distance between point of suspensionand
centre of mass.
T=2x
m
Torsional Pendulum
Smooth surface Time period (T: T= 2n where, C= Torsional constant
Superposition of two SHM s along the same direction
x,=A, sin ot
2 T-.
m m,
where is known as "reduced
(m, + m,) and x, = A, sin (ot + 0)
mass If equation of resultant SHM is taken as x=A sin (ot + )
m m.
A=J4; + A; + 24,4, cos 0
and tan =
A, sin
A, + A, cos
A
Combination of Springs
Series Combination:
Parallel combination: k, = k, + k,
Simple pendalum T- 2r A,
SHORT NOTES
Simple Harmonic Motion
F=-kx T V&
(in accelerating Reference Frame): gor is net
General equation of S.H.M. is x = A sin (ot + ): (ot + ) is phase acceleration due to pseudo force and gravitational force.
of the motion and is initial phase of the motion.
Time period of simple pendulum in Accelerating lift.
(i) If velocity of lift in constant,
T = 2rf
&efr8
Time period (T): T=
=2k
m
T-24 (.: a = 0)
(i) Iflif is moving upwards with acceleration a Br=8ta
Speed: v = aa
T=27
Acceleration: a = -o'x Vg+a
(iü) Iflift is moving downwards with acceleration a,
Kinetie Eaergy (KEN =mm (#-)-(4-+) Ber g-a
T-2 Vg-a
Potential Enegy (PE): kr=ma (iv) Iflift falls downwards freely,
Ber=0
Total Mechanical Energy (TME) T=0
= constant Compound Pendulum/Physical Pendulum
Spring-Mass System
Time Period (): T= 2r mgl
where, I = t ml'; lis distance between point of suspensionand
centre of mass.
T=2x
m
Torsional Pendulum
Smooth surface Time period (T: T= 2n where, C= Torsional constant
Superposition of two SHM s along the same direction
x,=A, sin ot
2 T-.
m m,
where is known as "reduced
(m, + m,) and x, = A, sin (ot + 0)
mass If equation of resultant SHM is taken as x=A sin (ot + )
m m.
A=J4; + A; + 24,4, cos 0
and tan =
A, sin
A, + A, cos
A
Combination of Springs
Series Combination:
Parallel combination: k, = k, + k,
Simple pendalum T- 2r A,
