Question

A particle executes SHM of amplitude 25 cm and time periods 3 s. what is the minimum time required for the particle to move between two points located at 12.5 cm on either side of the mean position?

Solution

Correct option is

0.5 s

Let A and B be the two extreme positions of the particle with O as the mean position. Displacements to the right of O are taken as positive while those to the left of O are taken as negative

                                                    

Let the displacement of the particle is SHM be given by 

                                             ..(i)

let us suppose that at time t = 0, the particle is at extreme position B. Setting x = A and t = 0 in Eq. (i) we have

                    A = A sin Ï•  

Giving          

  

                  

Where        A = 25 cm. 

Now let us say that the particle reaches point C at t = t1 and point D at t =t2. At C, the displacement x(t1) = + 12.5 cm and at D, it is x(t2) = –12.5 cm (see fig.) so from (ii) we have

                          

                

  

  

Notice that cos ωt2 = –0.5 even for  This value of t2 does not correspond to the minimum time because this is the time at which the particle, moving to left, reaches A and then returns to D.

SIMILAR QUESTIONS

Q1

The mass m shown in figure is displaced vertically by a small amount and released. If the system oscillates with a period of 2 seconds, the value of the spring constant k is

                                                              

Q2

A spring of force constant k is cut into three equal pieces. If these three pieces are connected in parallel, the force constant of the combination will be

Q3

Two springs of force constants k1 and k2 are connected as shown in figure. The time period of vertical oscillations of mass m is given by

                                                                

Q4

A sonometer wire of length 120 cm is divided into three segments of lengths in the ratio of 1 : 2 : 3. What is the ratio of their fundamental frequencies?

Q5

A particle is in linear simple harmonic motion between two extreme pointsA and B, 10 cm apart (see fig). If the direction from A to B is taken as positive direction, what are signs of displacement x, velocity V and acceleration a, when the particle is at A  

                                                

Q6

A simple harmonic motion of amplitude A has a time period T. The acceleration of the oscillator when its displacement is half the amplitude is

Q7

A body oscillates harmonically with amplitude 0.05 m. At a certain instant of time its displacement is 0.01 m and acceleration is 1.0 ms-2. What is the period of oscillation?

Q8

A tuning fork produces 4 beta per second when sounded with sonometer of vibrating length 48cm. It produces 4 beats per second also when the vibrating length is 50cm. What is the frequency of the tuning fork?

Q9

 

The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as 

                         

The magnitude of the maximum acceleration of the particle is 

Q10

A body executing linear simple harmonic motion has a velocity of 3 cms–1when its displacement is 4 cm and a velocity of 4 cms–1 when its displacement is 3 cm. what is the amplitude of oscillation?