Advertisements
Advertisements
Question
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
The rotation of the earth about its axis.
Advertisements
Solution
During its rotation about its axis, earth comes to the same position again and again in equal intervals of time. Hence, it is a periodic motion. However, this motion is not simple harmonic. This is because earth does not have a to and fro motion about its axis.
APPEARS IN
RELATED QUESTIONS
A seconds pendulum is suspended in an elevator moving with constant speed in downward direction. The periodic time (T) of that pendulum is _______.
A copper metal cube has each side of length 1 m. The bottom edge of the cube is fixed and tangential force 4.2x108 N is applied to a top surface. Calculate the lateral displacement of the top surface if modulus of rigidity of copper is 14x1010 N/m2.
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.
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)?

Answer in brief:
Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?
The total mechanical energy of a spring-mass system in simple harmonic motion is \[E = \frac{1}{2}m \omega^2 A^2 .\] Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will
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
Two bodies A and B of equal mass are suspended from two separate massless springs of spring constant k1 and k2 respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of A to that of B is
A particle moves in a circular path with a uniform speed. Its motion is
A particle is fastened at the end of a string and is whirled in a vertical circle with the other end of the string being fixed. The motion of the particle is
A body of mass 1 kg is mafe to oscillate on a spring of force constant 16 N/m. Calculate (a) Angular frequency, (b) Frequency of vibrations.
The period of oscillation of a body of mass m1 suspended from a light spring is T. When a body of mass m2 is tied to the first body and the system is made to oscillate, the period is 2T. Compare the masses m1 and m2
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)
Which of the following example represent periodic motion?
A freely suspended bar magnet displaced from its N-S direction and released.
Which of the following example represent periodic motion?
A hydrogen molecule rotating about its center of mass.
A simple pendulum of frequency n falls freely under gravity from a certain height from the ground level. Its frequency of oscillation.
The displacement time graph of a particle executing S.H.M. is shown in figure. Which of the following statement is/are true?

- The force is zero at `t = (T)/4`.
- The acceleration is maximum at `t = (4T)/4`.
- The velocity is maximum at `t = T/4`.
- The P.E. is equal to K.E. of oscillation at `t = T/2`.
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?
