Advertisements
Advertisements
प्रश्न
The equation of motion of a particle is x = a cos (αt)2. The motion is ______.
पर्याय
periodic but not oscillatory.
periodic and oscillatory.
oscillatory but not periodic.
neither periodic nor oscillatory.
उत्तर
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
संबंधित प्रश्न
Which of the following example represent periodic motion?
An arrow released from a bow.
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
General vibrations of a polyatomic molecule about its equilibrium position.
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 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
The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitude 2 cm, 1 m s−1 and 10 m s−2 at a certain instant. Find the amplitude and the time period of the motion.
A uniform disc of radius r is to be suspended through a small hole made in the disc. Find the minimum possible time period of the disc for small oscillations. What should be the distance of the hole from the centre for it to have minimum time period?
A 20 cm wide thin circular disc of mass 200 g is suspended to rigid support from a thin metallic string. By holding the rim of the disc, the string is twisted through 60° and released. It now performs angular oscillations of period 1 second. Calculate the maximum restoring torque generated in the string under undamped conditions. (π3 ≈ 31)
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.
When two displacements represented by y1 = a sin(ωt) and y2 = b cos(ωt) are superimposed the motion is ______.
A simple pendulum of frequency n falls freely under gravity from a certain height from the ground level. Its frequency of oscillation.
