Advertisements
Advertisements
Question
The equation of motion of a particle is x = a cos (αt)2. The motion is ______.
Options
periodic but not oscillatory.
periodic and oscillatory.
oscillatory but not periodic.
neither periodic nor oscillatory.
Advertisements
Solution
The equation of motion of a particle is x = a cos (αt)2. The motion is oscillatory but not periodic.
Explanation:
As the given equation is x = a cos (αt)2 is a cosine function. Hence, it is an oscillatory motion.
Now, putting t + T in place of t
x(t + T) = a cos [α(t + T)]2 .....[∵ x(t) = a cos(αt)2]
= a cos[αt2 + αT2 + 2α t T] ≠ x (t)
Where T is supposed as a period of the function ω(t).
Hence, it is not periodic.
APPEARS IN
RELATED QUESTIONS
Figure depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?
The length of the second’s pendulum in a clock is increased to 4 times its initial length. Calculate the number of oscillations completed by the new pendulum in one minute.
A particle executes simple harmonic motion with a frequency v. The frequency with which the kinetic energy oscillates is
A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will
Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.
The string the spring and the pulley shown in figure are light. Find the time period of the mass m.
The left block in figure moves at a speed v towards the right block placed in equilibrium. All collisions to take place are elastic and the surfaces are frictionless. Show that the motions of the two blocks are periodic. Find the time period of these periodic motions. Neglect the widths of the blocks.
The ear-ring of a lady shown in figure has a 3 cm long light suspension wire. (a) Find the time period of small oscillations if the lady is standing on the ground. (b) The lady now sits in a merry-go-round moving at 4 m/s1 in a circle of radius 2 m. Find the time period of small oscillations of the ear-ring.
Find the number of oscillations performed per minute by a magnet is vibrating in the plane of a uniform field of 1.6 × 10-5 Wb/m2. The magnet has a moment of inertia 3 × 10-6 kg/m2 and magnetic moment 3 A m2.
Which of the following example represent periodic motion?
A hydrogen molecule rotating about its center of mass.
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
A motion of an oscillating mercury column in a U-tube.
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
The motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lowermost point.
When two displacements represented by y1 = a sin(ωt) and y2 = b cos(ωt) are superimposed the motion is ______.
What are the two basic characteristics of a simple harmonic motion?
Show that the motion of a particle represented by y = sin ωt – cos ωt is simple harmonic with a period of 2π/ω.
A person normally weighing 50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 2.0 s–1 and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time.
- Will there be any change in weight of the body, during the oscillation?
- If answer to part (a) is yes, what will be the maximum and minimum reading in the machine and at which position?
A person normally weighing 50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 2.0 s–1 and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time.
- Will there be any change in weight of the body, during the oscillation?
- If answer to part (a) is yes, what will be the maximum and minimum reading in the machine and at which position?
When a particle executes Simple Harmonic Motion, the nature of the graph of velocity as a function of displacement will be ______.
