Representing and Analyzing SHM AP Physics C Mechanics MCQ – Exam Style Questions etc.
Representing and Analyzing SHM AP Physics C Mechanics MCQ
Unit 7: Oscillations
Weightage : 10-15%
Question
Systems A and B contain identical ideal springs and identical blocks that can slide along a surface of negligible friction. In system A, the surface is horizontal. In system B, the surface makes an
angle q with the horizontal. Initially, both blocks are at rest and in equilibrium. Each block is then pulled the same distance d in the direction shown in the figures and released from rest at t = 0.
After the block in system A is released from rest, the time for the block to first reach a maximum speed is\( \Delta t_A\). After the block in system B is released, the time for the block to first reach a maximum speed is
(A) \( \Delta t_A\)
(B) \(\Delta t_A\) (sin \theta)\)
(C) \(\Delta t_A\) (sin \theta)\)
(D)\(\Delta t_A\) (cos \theta)\)
(E) \(\Delta t_A\) (cos\theta)\)
Answer/Explanation
Ans:A
Since orientation does not affect the period of oscillation of the spring-block system, the time to reach maximum speed will be the same for system B as it was for system A.
Question
A 2.0 kg block is attached to a string that passes over a pulley and is attached to an ideal spring of spring constant k = 100 N m, as shown above. The pulley and string have negligible mass, and there is negligible friction in the pulley. The block is held in place with the spring at its original unstretched length and then released from rest. The amplitude of the resulting oscillation is most nearly
(A) 4.0 cm
(B) 2.0 cm
(C) 10 cm
(D) 20 cm
(E) 40 cm
Answer/Explanation
Ans:D
The spring begins unstretched. To determine the amplitude of oscillation, Newton’s second law can be used to determine how far the block will now stretch the spring to the equilibrium position. Substituting into Newton’s second law yields
Question
A block of mass M is suspended from two identical springs of negligible mass, spring constant kand unstretched length L. First, one spring is attached to the end of the other spring.
The block is then attached to the end of the second spring and slowly lowered to its equilibrium position. The two springs stretch a total distance of \(X_1\) , as shown in Figure 1 above. Next, the springs are hung side by side. The block is attached to the end of the springs and again slowly lowered to its equilibrium position. The springs each stretch a distance of \(X_2\) , as shown
in Figure 2 above. Which of the following equations correctly shows the relationship between \(X_1\) and \(X_2\) ?
(A)\(X_1=X_2\)
(B)\(X_1=\sqrt{2X_2}\)
(C)\(X_1=2X_2\)
(D)\(X_1=4X_2\)
(E)\(X_1=8X_2\)
Answer/Explanation
Ans:D
Question
A 1.0 kg mass is attached to the end of a vertical ideal spring with a force constant of 400 N/m. The mass is set in simple harmonic motion with an amplitude of 10 cm. The speed of the 1.0 kg mass at the equilibrium position is
(A)2 m/s
(B)4 m/s
(C)20 m/s
(D) 40 m/s
(E) 200 m/s
Answer/Explanation
Ans:A