Question

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

                                                                

Solution

Correct option is

 

Two springs are connected in parallel. Therefore, the force constant of the combination is 

                       

This can be shown as follows: Let x be the extension in each spring. Since the total force is mg, the restoring force in each spring has a magnitudemg/2. 

 . Therefore  

                                    

SIMILAR QUESTIONS

Q1

 

A simple harmonic motion is given by the equation 

               

Where x is in metres. The amplitude of the motion is

Q2

Figure shows three identical springs A, B, C. When a 4 kg weight is hung on A, it descends by 1 cm. When a 6 kg weight is hung on C, it will descent by

                                                   

Q3

A spring of force constant k is cut into two equal halves. The force constant of each half is

Q4

Two springs of equal lengths and equal cross-sectional areas are made of materials whose Young’s modulii are in the ratio of 3:2. They suspended and loaded with the same mass. When stretched and released, they will oscillate with time periods in the ratio of

Q5

Two bodies A and B of equal masses are suspended from two separate springs of force constants k1 and k2 respectively. If the two bodies oscillate such that their maximum velocities are equal, the ratio of the amplitudes of oscillation of A and B will be

Q6

Two springs A and B have force constants k1 and k2 respectively. The ratio of the work done on A to that done on B in increasing their lengths by the same amount is

Q7

Two springs A and B have force constants k1 and k2 respectively. The ratio of the work done on A to that done on B when they are stretched by the same force is

Q8

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

                                                              

Q9

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

Q10

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?