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Chapter 15: Q.1 (page 414)

A block oscillating on a spring has period T=2s. What is the period if:

a. The block's mass is doubled?Explain. Note that you do not know the value of either mor k, so do not assume any particular values for them. The required analysis involves thinking about ratios.

b. The value of the spring constant is quadrupled?

c. The oscillation amplitude is doubled while and kare unchanged?

Short Answer

Expert verified

a.The period is 2.828swhen block's mass is doubled.

b.The time if the spring constant is quadrupled is 1s.

c.The oscillation amplitude is double whilemandkchange time period.

Step by step solution

01

Formula for time

Use the following Formula to find the time.

T=2蟺mk

Here, mis the mass and kis the spring constant.

02

Calculation of time (part a)

The initial time

T=2蟺mk鈰�鈰�路(1)

If the block mass is blocked, then m=2mand new time T'

T'=2蟺2mk

T'=22蟺mk

From equation (1)the above equation will be,

T'=2T

Substitute 2sfor Tin the above equation

T'=2(2s)

T'=2.828s

03

Calculation for time if the spring constant is quadrupled (part b)

b)

If the value of spring constant is quadrupled, then new time T'is,

T'=2蟺m4k

T'=122蟺mk

T'=12T

Substitute 2sfor Tin the above equation.

T'=12(2s)

T'=1s

04

Oscillation amplitude changes (part c)

c) Time doesn't depend on oscillation amplitude, until and unless m and k change time period.

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Most popular questions from this chapter

IA 2.0g spider is dangling at the end of a silk thread. You can make the spider bounce up and down on the thread by tapping lightly on his feet with a pencil. You soon discover that you can give the spider the largest amplitude on his little bungee cord if you tap exactly once every second. What is the spring constant of the silk thread?

A250g air-track glider is attached to a spring with spring constant 4.0N/m. The damping constant due to air resistance is 0.015kg/s. The glider is pulled out 20cm from equilibrium and released. How many oscillations will it make during the time in which the amplitude decays to e-1 of its initial value?

Your lab instructor has asked you to measure a spring constant using a dynamic method鈥攍etting it oscillate鈥攔ather than a static method of stretching it. You and your lab partner suspend the spring from a hook, hang different masses on the lower end, and start them oscillating. One of you uses a meter stick to measure the amplitude, the other uses a stopwatch to time 10oscillations.

Your data are as follows:

Use the best-fit line of an appropriate graph to determine the spring constant.

A spring is standing upright on a table with its bottom end fastened to the table. A block is dropped from a height 3.0 cm above the top of the spring. The block sticks to the top end of the spring and then oscillates with an amplitude of 10 cm. What is the oscillation frequency?

The analysis of a simple pendulum assumed that the mass was a particle, with no size. A realistic pendulum is a small, uniform sphere of mass Mand radius Rat the end of a massless string, withLbeing the distance from the pivot to the center of the sphere.

a. Find an expression for the period of this pendulum.

b. SupposeM=25g,R=1.0cm,andL=1.0m, typical values for a real pendulum. What is the role="math" localid="1650084928460" Treal/Tsimpleratio, whererole="math" localid="1650084943350" Trealis your expression from part a androle="math" localid="1650084959286" Tsimple is the expression derived in this chapter?
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