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Chapter 15: Q. 18 (page 415)

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?

Short Answer

Expert verified

a) The amplitude of the subsequent oscillations is A=10.0cm

b) The block speed at the point when x=12Ais v=34.64cm/s

Step by step solution

01

Given data.

Given:

  • m=1.0kg
  • k=16N/m
  • v(0)=40cm/s
  • x(0)=0

Required:

(a) A

(b)vwhenx=12A

02

Simplification.

a) using conservation law and simplify to get that

v=蝇A2-x2鈬�A2=(v蝇)2+x2鈬�(1)

All is known except 蝇which is given by

蝇2=km鈬�(2)

substitution in (2)to get that

蝇2=161=16鈬�蝇=4rad/s

substitution in (1)to get that

A2=0.442鈬�A=0.1m=10.0cm

03

Using equation (1)

To get

v=4102-52=34.64cm/s

Where :

x=A/2=10/2=5cm

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