A 160 g block attached to a spring with spring constant 2.2 N/m oscillates horiz

Question

A 160 g block attached to a spring with spring constant 2.2 N/m oscillates horizontally on a frictionless table. Its velocity is 24 cm/s when x0 = -4.3 cm .

A 160 g block attached to a spring with spring constant 2.2 N/m oscillates horizontally on a frictionless table. Its velocity is 24 cm/s when x0 = -4.3 cm .

What is the amplitude of oscillation?

Express your answer to two significant figures and include the appropriate units.

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Part B

What is the block's maximum acceleration?

Express your answer to two significant figures and include the appropriate units.

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Part C

What is the block's position when the acceleration is maximum?

Express your answer to two significant figures and include the appropriate units.

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Part D

What is the speed of the block when x1 = 2.7 cm ?

Express your answer to two significant figures and include the appropriate units.

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Explanation / Answer

mass of the block, m=160g

spring constant, K=2.2 N/m

w=sqrt(K/m)

w=sqrt(2.2/(160*10^-3))

w=3.71 rad/sec

===>

if x=-4.3 cm ===> v=24 cm/sec

a)

use,

v^2=w^2*(A^2-x^2)

0.24^2=3.71^2*(A^2-0.043^2)

=====> A=0.0777 m

or

amplitude, A=7.77cm

b)

a_max=w^2*A

a_max=(3.71)^2*(7.77*10^-2)

a_max=1.07 m/sec^2

C)

at extreme position, x=A=7.77 cm ===> a_max=1.07 m/sec

D)

if x=2.7cm

v^2=w^2*(A^2-x^2)

v^2=3.71^2*(0.077^2-0.027^2)

===>

v=0.27 m/sec

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