Advertisements
Advertisements
Question
What are the two basic characteristics of a simple harmonic motion?
Solution
The two basic characteristics of a simple harmonic motion:
- Acceleration is directly proportional to displacement.
- The direction of acceleration is always towards the mean position, which is opposite to displacement.
APPEARS IN
RELATED QUESTIONS
Which of the following example represent periodic motion?
An arrow released from a bow.
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)?
A small block of mass m is kept on a bigger block of mass M which is attached to a vertical spring of spring constant k as shown in the figure. The system oscillates vertically. (a) Find the resultant force on the smaller block when it is displaced through a distance x above its equilibrium position. (b) Find the normal force on the smaller block at this position. When is this force smallest in magnitude? (c) What can be the maximum amplitude with which the two blocks may oscillate together?
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?
The maximum speed of a particle executing S.H.M. is 10 m/s and maximum acceleration is 31.4 m/s2. Its periodic time is ______
Which of the following example represent periodic motion?
A swimmer completing one (return) trip from one bank of a river to the other and back.
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?
A particle performs simple harmonic motion with a period of 2 seconds. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is `1/a` s. The value of 'a' to the nearest integer is ______.
