When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion.
-Which one of the following statements is true concerning the motion of the block?
A)Its acceleration is constant.
B)The period of its motion depends on its amplitude.
C)Its acceleration is greatest when the spring returns to the 5.0 cm position.
D)Its velocity is greatest when the mass has reached its maximum displacement.
E)Its acceleration is greatest when the mass has reached its maximum displacement.

Question

When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.040 m to 0.045 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.15 m. The block is released at time t = 0 s and undergoes simple harmonic motion. 
-Which one of the following statements is true concerning the motion of the block?
A)Its acceleration is constant. 
B)The period of its motion depends on its amplitude. 
C)Its acceleration is greatest when the spring returns to the 5.0 cm position. 
D)Its velocity is greatest when the mass has reached its maximum displacement. 
E)Its acceleration is greatest when the mass has reached its maximum displacement.

Quizplus · Accepted Answer

The motion of the block is simple harmonic motion, which is characterized by the fact that the acceleration is proportional to the displacement from the equilibrium position and is directed towards the equilibrium position. Therefore, the acceleration is greatest when the mass has reached its maximum displacement, which is at the ends of its motion. This is because the displacement from the equilibrium position is greatest at these points. Thus, statement E is true. 
Statement A is false because the acceleration varies in simple harmonic motion. 
Statement B is false because the period of the motion only depends on the mass and spring constant, not the amplitude. 
Statement C is false because the acceleration is greatest at the ends of the motion. 
Statement D is false because the velocity is greatest at the equilibrium position, not at the ends of the motion.

When a 020-Kg Block Is Suspended from a Vertically Hanging Spring, It