Physics
Content
1
On a smooth horizontal ground, a small sphere of mass m is connected to two fixed points by two identical light springs each of force constant k. Figure 1.1 shows the TOP VIEW of the set-up. (Neglect air resistance.)
Figure 1.1 (a) The sphere is set into longitudinal oscillation along the x-direction and its displacement-time graph is shown in Figure 1.2.
Figure 1.2 (i)
What is the frequency of oscillation of the sphere?
(2 marks)
(ii)
The mass of the sphere is 0.2 kg. Find the force constant of each spring.
(3 marks)
(iii) When the sphere is at a position corresponding to point P on the displacement-time graph, what are the magnitude and direction of the restoring force acting on it? (3 marks) (iv) Sketch the variation of kinetic energy of the sphere with time. (No need to calculate the exact value of the kinetic energy.) (2 marks) (b) When the sphere is at the equilibrium position shown in Figure 1.1, each spring has a length L and an extension e. The sphere is now displaced slightly along the y-direction from its equilibrium position and released as shown in Figure 1.3. Assuming L and e remain almost unchanged, show that the subsequent motion of the sphere is simple harmonic with a 1 2ke frequency of . (4 marks) 2 π mL
Figure 1.3
On a smooth horizontal ground, a small sphere of mass m is connected to two fixed points by two identical light springs each of force constant k. Figure 1.1 shows the TOP VIEW of the set-up. (Neglect air resistance.)
Figure 1.1 (a) The sphere is set into longitudinal oscillation along the x-direction and its displacement-time graph is shown in Figure 1.2.
Figure 1.2 (i)
What is the frequency of oscillation of the sphere?
(2 marks)
(ii)
The mass of the sphere is 0.2 kg. Find the force constant of each spring.
(3 marks)
(iii) When the sphere is at a position corresponding to point P on the displacement-time graph, what are the magnitude and direction of the restoring force acting on it? (3 marks) (iv) Sketch the variation of kinetic energy of the sphere with time. (No need to calculate the exact value of the kinetic energy.) (2 marks) (b) When the sphere is at the equilibrium position shown in Figure 1.1, each spring has a length L and an extension e. The sphere is now displaced slightly along the y-direction from its equilibrium position and released as shown in Figure 1.3. Assuming L and e remain almost unchanged, show that the subsequent motion of the sphere is simple harmonic with a 1 2ke frequency of . (4 marks) 2 π mL
Figure 1.3
