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
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.
A simple harmonic motion is given by the equation
Where x is in metres. The amplitude of the motion is
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
A spring of force constant k is cut into two equal halves. The force constant of each half is
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
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
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
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
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
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
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?