Advertisements
Advertisements
Question
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`.
Advertisements
Solution
a, b and c
Explanation:
Consider the diagram
From the given diagram; it is clear that
- At `t = (3T)/4`, the displacement of the particle is zero. Hence. the particle executing SHM will be at the mean position ie., x = 0. So, acceleration is zero and force is also zero.
- At t = `(4T)/4`, displacement is maximum i.e., extreme position, so acceleration is maximum.
- At t = `T/4`, corresponds to the mean position. so velocity will be maximum at this position.
- At t = `(2T)/4 = T/2`, corresponds to extreme position, so KE = 0 and PE = maximum.
APPEARS IN
RELATED QUESTIONS
The periodic time of a linear harmonic oscillator is 2π second, with maximum displacement of 1 cm. If the particle starts from extreme position, find the displacement of the particle after π/3 seconds.
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 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.
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?
A person goes to bed at sharp 10.00 pm every day. Is it an example of periodic motion? If yes, what is the time period? If no, why?
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
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.
A particle of mass m is attatched to three springs A, B and C of equal force constants kas shown in figure . If the particle is pushed slightly against the spring C and released, find the time period of oscillation.
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.
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.
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.
A simple pendulum of frequency n falls freely under gravity from a certain height from the ground level. Its frequency of oscillation.
The equation of motion of a particle is x = a cos (αt)2. The motion is ______.
What are the two basic characteristics of a simple harmonic motion?
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 ______.
