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
If a force F is applied to a spring of force constant k and the spring extends by an amount x, then
The extension x produced in a spring is proportional to its length. Thus, if the spring is cut into three equal pieces, the same force F will produce an extension x/3 in a piece. If k’ is the force constant of the piece, we have
. Thus, the force constant of each piece is 3k. When springs are connected in parallel, the force constant of the combination is equal to the sum of the individual force constants of the springs so connected. Therefore, the force constant of the combination = 3k + 3k + 3k = 9k.
A mass M attached to a light spring oscillates with a period of 2 seconds. If the mass is increased by 2 kg the period increases by 1 second. What is the value of M?
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
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