Topic 14.1: Oscillatory Motion
Answer Key with Hints/Solutions
1. (b) Sol: One complete round trip about the mean position is defined as one vibration or cycle.
2.
(b) Sol: Frequency unit is Hertz (
) and dimension
is 
.
3.
(c) Sol: Since 
, option (c) is
correct.
4. (c) Sol: Energy carried by an oscillating body or wave depends on the square of its amplitude.
5.
(b) Sol: At the mean position, displacement 
, so restoring
force brings it to rest/equilibrium where 
.
6.
(d) Sol: From mean to extreme (
), back to mean
(), to opposite
extreme (), and back to
mean () totals 
.
7.
(c) Sol: Speeding up vibrations increases oscillations per second (
doubles) and reduces time per oscillation (
is halved).
8. (b) Sol: Oscillatory motion is defined as periodic to-and-fro motion about a fixed mean position.
9. (c) Sol: Plucking harder increases displacement from rest (amplitude), which increases the energy of the wave.
10.
(b) Sol: 
.
11.
(c) Sol: One-way motion extreme to extreme is half a cycle (
); thus full
period 
.
12.
(b) Sol: 
and 
.
13.
(b) Sol: 
; 
.
14.
(b) Sol: 
.
15.
(c) Sol: 
oscillations.
Topic 14.2 & 14.3: Simple Harmonic Motion & Practical S.H.M Systems (Mass Attached to an Elastic Spring & Simple Pendulum)
Answer Key with Hints/Solutions
1.
(b) Sol: In S.H.M., acceleration is directly proportional to
displacement and directed towards mean position (
).
2.
(c) Sol: Elastic force of spring 
acts as restoring force.
3.
(b) Sol: Weight component 
acts along tangent toward mean position.
4.
(c) Sol: By definition, a pendulum with period 
is a seconds pendulum.
5. (b) Sol: Body reaches maximum velocity at mean position and inertia carries it past equilibrium.
6. (b) Sol: S.H.M requires restoring force strictly proportional to displacement, which ECG signals do not follow.
7.
(b) Sol: Altitude increases, 
decreases; since 
, decreasing increases 
.
8.
(d) Sol: Frequency 
is independent of mass 
.
9.
(b) Sol: To keep constant when 
, length must
be 
.
10.
(b) Sol: Summer thermal expansion increases length 
, increasing . Decreasing
length shortens period back to normal.
11.
(b) Sol: Human ear hears 
. Pendulums
oscillate at 
(infrasonic).
12.
(a) Sol: 
; 
.
13.
(c) Sol: 
.
14.
(c) Sol: 
(
).
15.
(c) Sol: 
. If 
, 
.
Topic 14.4: Simple Harmonic Motion and Uniform Circular Motion
Answer Key with Hints/Solutions
1. (b) Sol: The projection of a particle moving uniformly along a circle onto its diameter executes S.H.M.
2.
(b) Sol: From triangle POQ, 
.
3.
(b) Sol: Linear tangential velocity in circular motion is 
.
4.
(b) Sol: Instantaneous velocity 
becomes zero when 
.
5.
(b) Sol: Centripetal acceleration 
projected horizontally gives 
, pointing to
mean position.
6.
(b) Sol: 
.
7.
(b) Sol: In 
, the negative
sign proves 
and 
act in opposite (antiparallel) directions.
8.
(a) Sol: 
. Replacing 
and 
yields 
.
9. (c) Sol: The shadow mimics the motion of the projection on a diameter, which is S.H.M.
10.
(b) Sol: At extreme position (), velocity 
and magnitude of acceleration 
is maximum.
11.
(c) Sol: Amplitude 
. Total path
length between extremes 
.
12.
(b) Sol: 
.
13.
(c) Sol: 
.
14.
(b) Sol: 
.
15.
(b) Sol: 
; 
.
Topic 14.5 & 14.6: Phase & Graphical Representation of S.H.M
Answer Key with Hints/Solutions
1.
(c) Sol: The angle 
is defined as the phase of the motion.
2.
(b) Sol: Graphically and mathematically, displacement 
and velocity 
have a phase difference of 
rad (
).
3.
(c) Sol: When phase difference is 
(
rad), systems oscillate completely out of
phase.
4.
(b) Sol: 
.
5.
(a) Sol: At 
, 
.
6.
(b) Sol: Velocity reaches its maximum value a quarter-cycle () ahead of
displacement, leading it by .
7.
(c) Sol: At 
, 
; acceleration 
.
8.
(b) Sol: Max displacement corresponds to phase 
or , mean position
corresponds to ; phase
difference is ().
9.
(b) Sol: Since 
, 
, meaning they
move with equal magnitude in opposite directions.
10.
(d) Sol: 
, which starts
at zero and moves positive at .
11.
(b) Sol: "In phase" means phase difference is 
or 
; both reach
identical motion states simultaneously.
12.
(b) Sol: 
. 
(taking magnitude as per textbook example
14.4).
13.
(b) Sol: 
.
14.
(b) Sol: 
.
15.
(b) Sol: 
. Since 
, 
.
Topic 14.7: Conservation of Energy in S.H.M
Answer Key with Hints/Solutions
1.
(b) Sol: Instantaneous potential energy of spring is 
.
2.
(c) Sol: At mean position , 
, so total
energy is purely kinetic (
).
3.
(b) Sol: Substituting 
into 
yields 
.
4.
(b) Sol: 
.
5.
(b) Sol: Equating 
.
6.
(c) Sol: 
. Doubling
amplitude (
) increases
total energy by 
times.
7.
(a) Sol: At 
, 
, so ratio is 
.
8.
(c) Sol: At , 
and 
; ratio 
(
).
9. (b) Sol: At extreme height, energy is potential; as it descends toward mean, potential converts to kinetic, peaking at lowest point.
10.
(b) Sol: ; energy is
directly proportional to spring constant 
.
11.
(a) Sol: At mean position, displacement relative to rest is zero, so
potential energy is 
and kinetic energy is 
.
12.
(b) Sol: 
.
13.
(a) Sol: 
.
14.
(b) Sol: 
.
15.
(b) Sol: 
; 
.
Topics 14.8 & 14.9: Free and Forced Oscillations & Damped Oscillation
Answer Key with Hints/Solutions
1. (b) Sol: By definition, free vibrations occur at natural frequency without external force interference.
2. (c) Sol: Oscillations whose amplitude decreases over time due to resistive forces are damped oscillations.
3. (c) Sol: Thick oil provides heavy viscous resistance, resulting in heavy damping.
4. (c) Sol: Critical damping returns a system to equilibrium in the shortest possible time without oscillating.
5. (c) Sol: Damping forces do work against motion, converting mechanical energy into thermal energy.
6. (b) Sol: In forced oscillations, the system vibrates at the driving frequency of the external force.
7. (b) Sol: Free oscillations depend only on natural frequency; forced oscillations depend on periodic driver forces.
8. (b) Sol: Air resistance and joint friction act as dissipating forces, reducing energy and bringing it to rest.
9. (b) Sol: Shock absorbers use fluid damping to achieve near-critical damping for smooth, comfortable rides.
10. (b) Sol: Running machinery exerts periodic external forces on the floor, producing forced vibrations.
11. (c) Sol: Vibrating strings drive the wooden body to vibrate forcibly at the same frequency.
12. (b) Sol: Damping causes amplitude to decay exponentially over time.
13. (b) Sol: Damping drag slightly slows motion, causing time period to increase slightly.
14. (c) Sol: Fingers absorb mechanical energy rapidly, causing heavy damping that stops vibration.
15. (c) Sol: Without energy dissipation, total mechanical energy and peak displacement (amplitude) stay constant.
Topic 14.10 & 14.11: Resonance, Sharpness of Resonance & Applications of Resonance & Standing Waves
Answer Key with Hints/Solutions
1. (b) Sol: Resonance occurs when external driving frequency equals natural frequency of the system.
2.
(b) Sol: Resonance condition extends to integral multiples: 
.
3. (b) Sol: Heinrich Rubens invented the Rubens flame tube to demonstrate acoustic standing waves.
4. (b) Sol: Sound pressure gradient forces trap small particles at standing wave nodes.
5. (b) Sol: Lower damping increases peak amplitude and sharpens the resonance curve.
6.
(b) Sol: Equal lengths give identical natural periods (
), causing
resonance transfer.
7. (a) Sol: Heavy damping dissipates energy quickly, reducing amplitude response across frequencies.
8. (b) Sol: Acoustic standing wave pressure variations govern gas flow rate out of drilled holes.
9. (b) Sol: Turning radio knob matches electrical circuit frequency to broadcast station frequency.
10. (b) Sol: Microwaves excite water molecules via resonance, generating heat through collisions.
11. (b) Sol: Wind-driven resonant vibrations built destructive oscillations in the suspension bridge.
12. (b) Sol: RF pulses resonate with atomic nuclei in strong magnetic fields to form MRI images.
13. (b) Sol: Sand shifts away from vibrating antinodes and settles on stationary nodal lines.
14. (b) Sol: Avoiding frequency overlap prevents dangerous resonant wing fluttering and destruction.
15. (b) Sol: Pith-ball has high surface-area-to-mass ratio, suffering higher damping than dense lead.
PHYSICS INN-ABDULLAH
SEEKHO PHYSICS WITH ABDULLAH
📚 Matric & Intermediate students — prep for MDCAT, entry tests, and other exams start here!
Get notes, past papers, MCQs, and test tips — all in one place.
Follow for daily updates:
🔗 Facebook: 1.PHYSICS INN
https://www.facebook.com/share/18Hd7Jfh5X/
2. SEEKHO PHYSICS WITH ABDULLAH
https://www.facebook.com/share/17doLZh9R1/
*Facebook profile*
https://www.facebook.com/share/18jyz3QRNB/
🔗 Instagram: https://www.instagram.com/physicsinn?igsh=Z2txMXRvMmFzaWo5
🔗 YouTube:
https://youtube.com/@physicsinn?si=5Bbfa4u6mNtsnQor
🔗 TikTok: https://www.tiktok.com/@physics.inn?_r=1&_t=ZS-96SNz0gik1S
🔗 WhatsApp channel : https://whatsapp.com/channel/0029Vb7eIraEwEjmvw0XTv2i
Don't miss next post — hit follow now! 🎯
0 Comments
IF YOU HAVE ANY DOUBT COMMENT IN COMMENT BOX