Consider a block of mass m attached to a spring with force constant k , as shown

Question

Consider a block of mass m attached to a spring with force constant k, as shown in the figure(Figure 1) . The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x=0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations.

Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.

part A After the block is released from x=A, it will

a.remain at rest.
b.move to the left until it reaches equilibrium and stop there.
c.move to the left until it reaches x=?A and stop there.
d.move to the left until it reaches x=?A and then begin to move to the right.

Part B The time it takes the block to complete one cycle is called the period. Usually, the period is denoted T and is measured in seconds.

The frequency, denoted f, is the number of cycles that are completed per unit of time: f=1/T. In SI units, f is measured in inverse seconds, or hertz (Hz).

If the period is doubled, the frequency is

Part C An oscillating object takes 0.10 s to complete one cycle; that is, its period is 0.10 s. What is its frequency f?

Express your answer in hertz.

Part D

If the frequency is 40 Hz, what is the period T ? (fig 2)

Express your answer in seconds.

Part E Which points on the x axis are located a distance A from the equilibrium position?

a. R only
b. Q only
c. both R and Q

Part F Suppose that the period is T. Which of the following points on the t axis are separated by the time interval T?

Part G

What is the period T ?

Express your answer in seconds.

Part H

How much time t does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement?

Express your answer in seconds.

Part I

What distance d does the object cover during one period of oscillation?

Express your answer in meters.

Part J

What distance d does the object cover between the moments labeled K and N on the graph?

Explanation / Answer

A)
since system is frictionless. Energy will be conserved and it will undergo simple harmonic motion
Answer: d.move to the left until it reaches x=A and then begin to move to the right.

B)
f = 1/T
if period doubles, frequency will become half
Answer: c.halved

C)
f = 1/T
   = 1/0.1
    = 10 Hz
Answer: 10 Hz

D)
T = 1/40
    =0.025 s
Answer : 0.025 s

I am allowed to answer only 4 parts at a time

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.