Simple Harmonic Motion

Question 1

What happens to a system performing SHM in reality?

Answer 1

It gradually loses its energy due to friction and air resistance.

Question 2

What is the motion called as the amplitude gradually becomes smaller and smaller?

Answer 2

Damped.

Question 3

What is the motion called if there is no damping and the amplitude remains constant?

Answer 3

Free.

Question 4

What is needed to maintain the free oscillation of a vibrating body for a long time?

Answer 4

An external periodic force.

Question 5

What are the oscillations of the body called in this case?

Answer 5

Forced vibration.

Question 6

What are vibrations resulting from the action of an external periodic force on an oscillating body called?

Answer 6

Forced vibrations.

Question 7

What does every object capable of vibrating possess?

Answer 7

A natural frequency (f₀) of vibration.

Question 8

What is natural frequency (f₀)?

Answer 8

The frequency with which the object will oscillate when it is left undisturbed after being set into vibration.

Question 9

What is the frequency of an external periodic force called?

Answer 9

The forcing frequency (f).

Question 10

What happens when the frequency of a vibrating body acting on a system coincides with the natural frequency of the system?

Answer 10

The system is set into vibration with a relatively large amplitude.

Question 11

What is this phenomenon called?

Answer 11

Resonance.

Question 12

Define resonance.

Answer 12

Resonance is said to occur when the forcing frequency (f) of an external periodic force coincides with the natural frequency (f₀) of a body with which it is in contact causing the body to vibrate with a large amplitude.

Question 13

What happens at resonance?

Answer 13

Maximum energy is transferred from the periodic external force to the natural vibrations of a system.

Question 14

Give examples of resonance.

Answer 14

Glass windows vibrating because of high-pitched notes from a radio set.

Question 15

What force is involved in the motion of an object in SHM?

Answer 15

A restoring force.

Question 16

What forms of energy are involved in SHM?

Answer 16

Kinetic energy (KE) and potential energy (PE).

Question 17

What is the total energy of a body performing SHM?

Answer 17

The sum of KE and PE and it is always conserved.

Question 18

Where is the energy all PE in a simple pendulum?

Answer 18

At the extreme positions R and L.

Question 19

What is the formula for PE?

Answer 19

PE = mgh.

Question 20

Where is PE = 0 in a simple pendulum?

Answer 20

At C.

Question 21

Where is KE maximum in a simple pendulum?

Answer 21

At C.

Question 22

What is the formula for maximum KE?

Answer 22

KE = 1/2 * mvₘ². where v_m is maximum velocity

Question 23

What is the relationship between maximum PE and maximum KE?

Answer 23

Maximum PE = maximum KE = (PE + KE) at any instant.

Question 24

What is the formula for v_m?

Answer 24

v_m = √(2gh).

Question 25

What is the total energy at any instant of motion of a simple pendulum?

Answer 25

Total energy = mgh + 1/2 * mv² = mgh_m = 1/2 * mv_m².

Question 26

What is the restoring force in a spring?

Answer 26

Elastic restoring force.

Question 27

What is the formula for elastic restoring force?

Answer 27

F = -Ky.

Question 28

What is the total work (W) done in stretching the spring a distance y?

Answer 28

W = 1/2 * Ky².

Question 29

What is the maximum total energy stored in the spring?

Answer 29

W = 1/2 * KA².

Question 30

What is the total energy at any stage of the oscillation?

Answer 30

W = 1/2 * KA² = 1/2 * mv² + 1/2 * Ky².

Question 31

What is the formula for v in terms of K m A and y?

Answer 31

v = √(K/m * (A² - y²)).

Question 32

What is the formula for K according to Hooke's law?

Answer 32

F = mg = Ke.

Question 33

What is the formula for ω?

Answer 33

ω = √(K/m).

Question 34

What is the formula for the period T?

Answer 34

T = 2π/ω = 2π√(m/K).

Question 35

What does the period (T) depend on?

Answer 35

The mass m and the force or elastic constant K.

Question 36

Does the period (T) depend on the amplitude of motion or the value of g?

Answer 36

No.

Question 37

What is the formula for the true value of the period T when the mass of the spring (m₀) is considered?

Answer 37

T = 2π√((m + m₀)/K).

Question 38

What is the formula for ω in terms of T?

Answer 38

ω = 2π/T.

Question 39

What is the formula for T in terms of ω?

Answer 39

T = 2π/ω.

Question 40

What is the formula for frequency f?

Answer 40

f = 1/T = ω/2π.

Question 41

What is the formula for ω in terms of f?

Answer 41

ω = 2πf.

Question 42

What is the angle θ swept through by the particle P as it moves round the circle once?

Answer 42

360° or 2π radians.

Question 43

What is the rate of change of the angle θ with time (t) called?

Answer 43

Angular velocity ω.

Question 44

Define angular velocity (ω).

Answer 44

The angle turned through by the body / time taken.

Question 45

What is the formula for angular velocity?

Answer 45

ω = θ/t.

Question 46

What is the formula relating distance uniform velocity and time?

Answer 46

s = vt or v = s/t.

Question 47

What is the unit of angular velocity?

Answer 47

Radians per second (rad/s).

Question 48

If the angle θ is changing with time what else is changing with time?

Answer 48

The arc length s = ZP.

Question 49

What is the formula for s?

Answer 49

s = rθ.

Question 50

What is the relationship between linear velocity (v) angular velocity (ω) and radius (r)?

Answer 50

v = ωr = ωA.

Question 51

What is the formula for linear velocity v at any point Q whose distance from C is x?

Answer 51

v = ω√(A² - x²).

Question 52

Where does the maximum velocity (vm) occur?

Answer 52

At x = 0.

Question 53

What is the maximum velocity (vm) at the central point or centre of motion?

Answer 53

vm = ωA.

Question 54

Where does the maximum velocity of SHM occur?

Answer 54

At the centre of motion (x = 0).

Question 55

Where does the minimum velocity of SHM occur?

Answer 55

At the extreme position of motion (x = A).

Question 56

What is the formula for acceleration (a)?

Answer 56

a = -ω²x.

Question 57

What does the negative sign in a = -ω²x indicate?

Answer 57

The acceleration a is directed towards the centre of motion while the displacement x is measured from that point outwards.

Question 58

What is the essential feature of SHM?

Answer 58

The acceleration and restoring force are always in a direction opposite to the displacement of the body and also the acceleration and force are always proportional to the displacement of the body from the central or equilibrium position.

Question 59

What is the formula for centripetal acceleration?

Answer 59

Centripetal acceleration = -v²/r = -v²/A.

Question 60

What is the relationship between linear acceleration (a) and angular acceleration (α)?

Answer 60

a = αr.

Question 61

What are some examples of simple harmonic motions?

Answer 61

The motion of the strings in a musical instrument eg guitar.

Question 62

What is the essential characteristic of oscillatory motion?

Answer 62

Regularity and repetition of motion.

Question 63

What is Simple Harmonic Motion (SHM)?

Answer 63

The periodic motion of a body or particle along a straight line such that the acceleration of the body is directed towards a fixed point or centre of motion and is also proportional to its displacement from that point.

Question 64

What is the relationship between acceleration restoring force and displacement in SHM?

Answer 64

Acceleration and restoring force are proportional to displacement and in the opposite direction.

Question 65

With what geometrical construction can we study simple harmonic motion?

Answer 65

A reference circle.

Question 66

What is the name of the point where the perpendicular from P meets the diameter YZ?

Answer 66

Q.

Question 67

What is the motion of Q along the diameter YZ?

Answer 67

Simple harmonic motion.

Question 68

What is the motion of P around the circle?

Answer 68

Constant speed v.

Question 69

What is the relationship between x A and θ?

Answer 69

x = A cos θ.

Question 70

What is the maximum value of x called?

Answer 70

The amplitude of the motion.

Question 71

Define amplitude (A) of a simple harmonic motion.

Answer 71

The maximum displacement of the body performing simple harmonic motion from its equilibrium or central position C.

Question 72

What is the period of SHM?

Answer 72

The total time taken by the point to move from Z to Y and back to Z.

Question 73

Define Period (T).

Answer 73

The total time taken by a vibrating body to make one complete revolution or cycle about a reference point.

Question 74

Define frequency (f).

Answer 74

The number of complete revolutions per second made by a vibrating body.

Question 75

What is the relationship between frequency and period?

Answer 75

f = 1/T.

Question 76

What is the SI unit of frequency?

Answer 76

Hertz (Hz).