π / ) x = cos ( π / – t ) x = sin ( π t + π / ) (d) x = cos π t . Figure . (a) shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end. A force F applied at the free end stretches the spring.
Figure . (b) shows the same spring with both ends free and attached to a mass m at either end. Each end of the spring in Fig. .
(b) is stretched by the same force F . Fig. . What is the maximum extension of the spring in the two cases ?
If the mass in Fig. (a) and the two masses in Fig. (b) are released, what is the period of oscillation in each case ? .
The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of . m. If the piston moves with simple harmonic motion with an angular frequency of rad/min, what is its maximum speed ? .
The acceleration due to gravity on the surface of moon is . m s – . What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is . s ?
( g on the surface of earth is . m s – ) . A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v .
If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period ? . A cylindrical piece of cork of density of base area A and height h floats in a liquid of density ρ l . The cork is depressed slightly and then released.
Show that the cork oscillates up and down simple harmonically with a period h g = π ρ ρ where ρ is the