SIMPLE HARMONIC MOTION
- A small mass is hung from the lower end of a vertical spring. The upper end of the spring is fixed. When the mass is displaced and then released, it oscillates with simple harmonic motion of amplitude 40mm and period 0.35s.
Calculate the velocity of the mass when the displacement is,
(a) zero
(b) +20mm.
2. The pistons of a car engine when idling move approximately in simple harmonic motion with amplitude 50mm and frequency 110Hz.
Calculate,
(a) the maximum speed of the pistons
(b) the maximum acceleration of the pistons.
3. A spiral spring is hung vertically from a fixed point. Its length when unloaded is 240mm.
(a) A 50g mass is hung from the lower end and its length increases to 300mm. Find the force constant of the spring.
(b) The mass is then pulled downwards and released. Find the period of the oscillations.
4. A small mass is placed on a scale pan supported by a spring. When the scale pan is displaced downwards then released, it oscillates with simple harmonic motion. Tests show that if the amplitude of oscillation is greater than a certain value, the mass leaves the scale at the highest point. If the period of the oscillation is 400ms, find the maximum amplitude at which the mass remains in contact with the pan at all times.
5. A trolley of mass 0.90kg on a horizontal runway has springs attached as shown below. A force of 2.5N is required to displace the trolley 50mm from the equilibrium position.
(a) Calculate the spring constant of the system.
(b) The trolley is released from rest 50mm from the equilibrium position. How long does it take to reach maximum displacement on the other side of equilibrium?
(c) What is its speed as it passes through equilibrium?
