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A periodic motion is one that is repeated at regular periods of time. Periodic motions include the hands of a clock, the earth’s orbit around the sun, and the moon’s orbit around the earth.
The body repeats the same set of movements over and over at equal intervals of time in this motion. An oscillation is a term for a set of movements like this.
A periodic time or period of revolution is the amount of time it takes to complete each set of movements or revolution.
Another type of periodic motion is when a particle moves to and fro around a mean point along the same path again. The motion of the prongs of a tuning fork, the pendulum in a clock, oscillations of springs, vibrations in stringed musical instruments such as the sitar, violin, etc., a child on a swing, vibrations of air columns, and so on are examples of oscillatory or vibratory motion.
The oscillating property is significant in many physical processes other than mechanics, such as how solid atoms vibrate around their mean or equilibrium positions.
Many biological instances of oscillations exist, such as the creation of sound by vocal chords and the oscillatory or vibratory action of insect wings.
Q1. The circular motion of a particle whose speed is constant is ________________
a) Periodic but not simple harmonic
b) Simple harmonic but not periodic
c) Periodic and simple harmonic
d) Neither periodic not simple harmonic
Answer: a) Periodic but not simple harmonic.
Although uniform circular motion is periodic, it is not simple harmonic.
Q2. A simple harmonic motion is defined as which of the following?
a) Ball bouncing between two vertical walls
b) Particle moving in a circle with uniform speed
c) Earth spinning about its axis
d) A wave travels through a string that is tied at both ends.
Answer: d) A wave travels through a string that is tied at both ends.
The nature of a wave travelling through a string with both ends fixed has a simple harmonic nature.
Q3. A particle moves along the x-axis in a basic harmonic motion. What is the source of the force operating on it?
a) Acos(kx)
b) Ae(-kx)
c) Akx
d) –Akx
Answer: d) –Akx.
F=-Akx denotes a proportionate or displacement force acting in the opposite direction. As a result, it symbolises simple harmonic motion.
Q4. Which of the following is a good example of simple harmonic motion?
a) Acceleration = kx
b) Acceleration = k0x + k1x2
c) Acceleration = -k (x+a)
d) Acceleration = k (x+a)
Answer: c) Acceleration = -k (x+a).
Acceleration = -kX, X = x+a.
As a result, the acceleration is proportional to the displacement and acts in the opposite direction of the displacement. As a result, basic harmonic motion is represented by acceleration = -k(x+a).
Q5. A particle executing simple harmonic motion of amplitude 5cm has a maximum speed of 31.4 cm/s. The frequency of its oscillation is?
a) 4Hz
b) 3Hz
c) 2Hz
d) 1Hz
Answer: d) 1Hz
vmax = 2πvA,
31.4=2×3.14v×5
v=1Hz.
Q6. A particle executes simple harmonic oscillation. Its amplitude is a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from its equilibrium position will be
a) T/8
b) T/12
c) T/2
d) T/4
Answer: b) T/12.
y = asinωt,
a/2 = asin(2πt/T),
sin(2πt/T) = sin(π/6)
2πt/T = π/6, t = T/12.
Q7. A simple harmonic oscillator has an amplitude A and time period T. The time require by it to travel from x = A to x = A/2 will be
a) T/6
b) T/4
c) T/3
d) T/2
Answer: a) T/6.
As the oscillator starts at x=A, we can consider
x=acosωt a/2 = acos(2πt/T) cos(2πt/T) = 1/2 = cos(π/3)
(2πt/T = π/3 or t = T/6).
Q8. If a simple harmonic oscillator has got a displacement of 0.02m and acceleration equal to 2m/s2 at any time, the angular frequency of the oscillator is equal to ___________
a) 10 rad/s
b) 0.1 rad/s
c) 100 rad/s
d) 1 rad/s
Answer: a) 10 rad/s.
a = -ω2y,
ω2 = a/y = 2/0.02 = 100
ω = 10rad/s.
Q9. What is the phase difference between a particle’s acceleration and its instantaneous velocity while it is performing simple harmonic motion?
a) π
b) 0.707π
c) Zero
d) 0.5π
Answer: d) 0.5π.
A particle executing simple harmonic motion has a phase gap of π/2 between its instantaneous velocity and acceleration.
Q10. Which one of the following statements is true for the speed v and the acceleration of a particle executing simple harmonic motion?
a) When v is zero, a is zero
b) Whatever the value of v is, the value of a is zero.
c) When v is maximum, a is zero
d) When c is maximum, a is maximum
Answer: c) When v is maximum, a is zero.
Acceleration is in phase with velocity by π/2 rad in a simple harmonic motion. As a result, when velocity is at its highest, acceleration is also at its lowest, and vice versa.
Q11. Which is the wrong statement from the following?
(a) We consider a force in a fixed direction in rectilinear motion (along the direction of motion of the body).
(b) We examine a force with a constant magnitude but variable direction in U.C.M.
(c) We examine a force with a constant magnitude and direction in S.H.M.
(d) We examine a force with variable magnitude and direction in S.H.M.
Answer: (c) We examine a force with a constant magnitude and direction in S.H.M.
Q12. Which of the following motions isn’t a simple harmonic linear motion?
(a) Motion of a magnet in a vibration magnetometer.
(b) Vertical motion of a body tied to a spring.
(c) Motion of the needle in a sewing machine.
(d) Simple pendulum motion for minor oscillations.
Answer: (a) Motion of a magnet in a vibration magnetometer.
Q13. For S.H.M., which of the following is a necessary and sufficient condition?
(a) proportionality between acceleration and displacement from equilibrium position
(b) constant period
(c) proportionality between restoring force and displacement from equilibrium position
(d) constant acceleration
Answer: (c) proportionality between restoring force and displacement from equilibrium position.
Q14. The application where a crystal oscillator is most likely to be found is
(a) Radio receiver
(b) Radio transmitter
(c) AF sweep generator
(d) None of the above
Answer: (b) Radio transmitter.
Q15. An oscillator differs from an amplifier because it
(a) Has more gain
(b) Requires no input signal
(c) Requires no d.c. supply
(d) Always has the same input
Answer: (b) Requires no input signal.
