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Tuesday, 19 November 2013

F.Sc Notes: Physics XI: Chapter 07 Oscillations Exercise Short Questions:

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

Question 7.1 Name two characteristics of simple harmonic notion (SHM)?
Answers 7.1
Characteristics of simple harmonic motion are as follow
  1. Simple harmonic motion is a vibrating motion.
  2. Acceleration is directly proportional to displacement.
  3. Acceleration is always directed towards mean position.

Question 7.2 Does frequency depends on amplitude for harmonic oscillators?
Answer 7.2
No, frequency is independent of amplitude it depends on Time period
                                          Time Period = T = 1/f.

Question 7.3 Can we realize an ideal simple pendulum?
Answer 7.3
No, because a friction less system cannot be made. We need 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 7.4
As T  is the time period for one complete vibration. Its maximum displacement,
                    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 7.5
    For simple pendulum,                
                                                      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 7.6 
No acceleration depends upon displacement x. As the relation between acceleration and displacement is 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.

Question 7.7 What is meant by phase angle? Does it define angle between maximum displacement and the driving force?
Answer 7.7
Phase angle (or phase): “The angle θ = wt which specifies the displacement as well as the direction of motion of the point executing SHM”.
It indicates the:
  1. State of motion of a vibrating particle
  2. 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 7.8
When there is a constant phase difference in amplitude and frequency are same. Exp are 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 7.9
For SHM. v = ω √ ( xo2 – x2) & a = - ω2 x .
  1. At mean position, from the above equations, x = 0 then a = 0 & v = ω xo i.e. acceleration is zero and velocity is maximum.
  2. 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:
  1. y = A sin (ω t + ϕ )
  2. a = - ω2 x
Answers 7.10
  1. 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.
  2. 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 7.11 
  For a body executing SHM. 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 7.12
Important role of resonance:
  1.     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.
  2.     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.
  3.     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.
  4.     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 7.13
Mass spring system is hung vertically and set into oscillations, the motion eventually stop due to energy dissipation, friction and damping.

Written By: Asad Hussain