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Chapter 15: Q. 4 (page 415)

An object in SHM oscillates with a period of 4.0sand an amplitude of 10cm. How long does the object take to move from x=0.0cm to x=6.0cm?

Short Answer

Expert verified

To move from x=0.0cmto x=6.0cm, the total time taken is 0.4s.

Step by step solution

01

Given Information 

Time period, T=4s.

The amplitude,A=10cm.

02

:Formula used 

Equation of the simple harmonic motion is x=Asin蝇t.

Where, at time t, xis the position, Ais the amplitude and蝇is the angular frequency.

03

Calculation 

Substitute the values to obtaint.

6=10sin2蟺T脳t610=sin2蟺4脳tsin-10.6=蟺2脳tt=0.4s
04

Final Answer 

To move from x=0.0cmto x=6.0cm, the total time taken is 0.4s.

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Most popular questions from this chapter

A penny rides on top of a piston as it undergoes vertical simple

harmonic motion with an amplitude of 4.0cm . If the frequency

is low, the penny rides up and down without difficulty. If the

frequency is steadily increased, there comes a point at which the

penny leaves the surface

a. At what point in the cycle does the penny first lose contact

with the piston?

b. What is the maximum frequency for which the penny just

barely remains in place for the full cycle?

FIGUREQ15.4shows a position-versus-time graph for a particle in SHM.

a. What is the phase constant 蠒0? Explain.

b. What is the phase of the particle at each of the three numbered points on the graph?

FIGUREQ15.3shows a position-versus-time graph for a particle in SHM. What are (a) the amplitude A, (b) the angular frequency 蝇, and the phase constant 蠒0?

A 1.0kgblock is attached to a spring with spring constant 16N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives its a speed of 40cm/s.

What are

a. The amplitude of the subsequent oscillations?

b. The block's speed at the point where x=12A?

An air-track glider attached to a spring oscillates between the 10cm mark and the 60cm mark on the track. The glider completes 10 oscillations in 33s. What are the (a) period, (b) frequency, (c) angular frequency, (d) amplitude, and (e) maximum speed of the glider?
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