Question

Answer each question and justify your answer in one or two sentences.

Question 1

A block is attached to the end of a horizontal ideal spring and rests on a frictionless surface. The other end of the spring is attached to a wall. The block is pulled away from the spring’s unstrained position by a distance x₀ and given an initial speed of v₀ as it is released. Which one of the following statements concerning the amplitude of the subsequent simple harmonic motion is true?

a) The amplitude will depend on whether the initial velocity of the block is in the +x or the -x direction.

b) The amplitude will be less than x₀.

c) The amplitude will be equal to x₀.

d) The amplitude will be greater than x₀.

e) The amplitude will depend on whether the initial position of the block is in the +x or the -x direction relative to the unstrained position of the spring.

Question 2

Object A is attached to ideal spring A and is moving in simple harmonic motion. Object B is attached to ideal spring B and is moving in simple harmonic motion. The period and the amplitude of object B are both two times the corresponding values for object A. How do the maximum speeds of the two objects compare?

a) The maximum speed of A is one fourth that of object B.

b) The maximum speed of A is one half that of object B.

c) The maximum speed of A is the same as that of object B.

d) The maximum speed of A is two times that of object B.

e) The maximum speed of A is four times that of object B.

Answer 1

Question 1) c) The amplitude will be equal to x0.

The remaining all options are false.

The amplitude does not depend on whether the initial velocity of the block is in the +x or the -x direction.
The amplitude does not depend on whether the initial position of the block is in the +x or the -x direction relative to the unstrained position of the spring.

on applying coservation of energy

(1/2)*k*A^2 = (1/2)*k*xo^2 + (1/2)*m*v^2

clearly, A > xo

Question 2) c) The maximum speed of A is the same as that of object B.

TB = 2*TA

A_B = 2*A_A

vA_max = A_A*wA

= A_A*(2*pi/TA)

vB_max = A_B*wB

= 2*A_A*(2*pi/TB)

= 2*A_A*(2*pi/(2*TA))

= A_A*(2*pi/TA)

= vA_max