## FSc Notes: Physics XI: Chapter 07 Oscillations Exercise SQ:

**Question 7.1 Name two characteristics of simple harmonic notion (SHM)?**

Answers 7.1Characteristics of simple harmonic motion are as follow

Answers 7.1

- Simple harmonic motion is a vibrating motion.
- Acceleration is directly proportional to displacement.
- Acceleration is always directed towards mean position.

**Question 7.2 Does frequency depends on amplitude for harmonic oscillators?**

Answer 7.2No, frequency is independent of amplitude it depends on Time period

Answer 7.2

**Time Period = T = 1/f.**

**Question 7.3 Can we realize an ideal simple pendulum?**

Answer 7.3No, because a friction less system cannot be made. We need

Answer 7.3

**mass less bob**,

**in-extensible string**and suspend it from a

**friction less support**.

**Question 7.4 What is the total distance traveled by an object moving with SHM in a time equal to its period, if its amplitude is A?**

Answer 7.4As T is the time period for one complete vibration. Its maximum displacement,

Answer 7.4

**xo = r = A. so total distance traveled will be 4A.**

**Question 7.5 What happens to the period of a simple pendulum if its length is doubled? What happens if the suspended mass is doubled?**

Answer 7.5For simple pendulum,

Answer 7.5

**T = 2π√( l / g)**

As the length is doubled so

**l = 2l**

**T = 2π√ (2 l / g) = √2 x 2π√ l / g = √2 T**

So

**the time period increases by √2 (=1.414) times, as length is doubled.**

**There will be no change, when suspended mass is doubled. As time period, T Time Period is independent of mass m**.

**Question 7.6 Does the acceleration of a simple harmonic oscillator remain constant during its motion? Is the acceleration ever zero? Explain.**

Answer 7.6No acceleration depends upon displacement x. As the relation between acceleration and displacement is

Answer 7.6

**a = -w(2)x.**

**The acceleration is zero at mean position i.e. (x=0), and maximum at extreme position (x=xo) .So,**

acceleration does not remain constant during motion.

acceleration does not remain constant during motion.

**Question 7.7 What is meant by phase angle? Does it define angle between maximum displacement and the driving force?**

Answer 7.7Phase angle (or phase): “The angle θ = wt which specifies the displacement as well as the direction of motion of the point executing SHM”.

Answer 7.7

It indicates the:

- State of motion of a vibrating particle
- Direction of motion of a vibrating particle.

**No. It does not define angle between maximum displacement and the driving force.**

**Question 7.8 Under what conditions the addition of two simple harmonic motions does produces a resultant. Which is also simple harmonic?**

Answer 7.8When there is a constant phase difference in amplitude and frequency are same. Exp are

Answer 7.8

**interference and beats.**

**Question 7.9 Show that in SHM the acceleration is zero when the velocity is greatest and the velocity is zero when the acceleration is greatest?**

Answer 7.9For SHM. v = ω √ ( xo2 – x2) & a = - ω2 x .

Answer 7.9

- At mean position, from the above equations, x = 0 then a = 0 & v = ω xo i.e. acceleration is zero and velocity is maximum.
- At extreme positions x = xo then v = 0 & a = -ω xo. i. e. velocity is zero when acceleration is maximum.

Question 7.10 In relation to SHM, explain the equations:

Question 7.10 In relation to SHM, explain the equations:

- y = A sin (ω t + ϕ )
- a = - ω2 x

**Answers 7.10**

**y = A sin (ω t + ϕ).**ϕ initial phase, y Instantaneous displacement, A Amplitude time t, (ω t + ϕ) State of motion.**This equation shows that displacement of SHM as a function of amplitude and phase angle depending upon time.****a = - ω2 x**where a = acceleration of a particle executing SHM ω = constant angular frequency x=instantaneous displacement from the mean position.**This equation shows that acceleration is directly proportional to displacement and is directed towards mean position.**

**Question 7.11 Explain the relation between total energy, potential energy and kinetic energy for a body oscillating with SHM.**

Answer 7.11For a body executing SHM.

Answer 7.11

**Etotal=P.E+K.E**. Since Total energy of SHM remains constant in the absence of frictional forces, the K.E and P.E interchange continuously from one form to another.

**At mean position, the energy is totally K.E. P.E = 0. In between it is partially P.E and K.E.**

**Question 7.12 Describe some common phenomena in which resonance plays an important role.**

Answer 7.12Important role of resonance:

Answer 7.12

- Microwave oven Microwaves (of frequency 2450 MHz) with λ = 12 cm, are absorbed due to resonance by water and fat molecules in the food, heating them up and so cooking the food.
- Children’s swing In order to raise the swing to a great height, we must give it a push at the right moment and in the right direction.
- Musical instruments in some instruments (e.g. drums) air columns resonate in the wooden box. In string instruments (e.g. sitar) strings resonate with their frequencies and loud music is heard.
- Tuning radio/TV we change the frequency with knob. When it becomes equal to a particular transmitted station, resonance occurs. Then we receive amplified audio/video signals.

**Question 7.13 If a mass spring system is hung vertically and set into oscillations, why does the motion eventually stop?**

Answer 7.13Mass spring system is hung vertically and set into oscillations, the motion eventually stop due to energy dissipation, friction and damping.

Answer 7.13