A block rests on a flat plate that executes vertical simple harmonic motion with a period of 0.74 s. What is the maximum amplitude of the motion for which the block does not separate from the plate? The acceleration of gravity is 9.8 m/s 2 . Answer in units of m.

Answer :

Answer:

maximum amplitude  = 0.13 m

Explanation:

Given that

Time period T= 0.74 s

acceleration of gravity g= 10 m/s²

We know that time period of simple harmonic motion given as

[tex]T=\dfrac{2\pi}{\omega}[/tex]

[tex]0.74=\dfrac{2\pi}{\omega}[/tex]

ω = 8.48 rad/s

ω=angular frequency

Lets take amplitude = A

The maximum acceleration given as

a= ω² A

The maximum acceleration should be equal to g ,then block does not separate

a= ω² A

10= 8.48² A

A=0.13 m

maximum amplitude  = 0.13 m

batolisis

The maximum amplitude of the motion for which the block does not separate from the plate is : 0.14 m

Given data :

period ( T ) = 0.74 secs

acceleration due to gravity ( g ) = 9.8 m/s62

Determine the maximum amplitude of the motion

Time period of simple harmonic motion ( T ) = [tex]\frac{2\pi }{w}[/tex]

First step : solve for w

w = 2π / T

   = 2π / 0.74

   = 8.49 rad/sec

Next step : determine the maximum amplitude ( A )

a = w² A

where ;  a = maximum acceleration = 9.8 , w = 8.49

therefore

A = a / w²

   = 9.8 / ( 8.49 )²

   = 0.136  ≈ 0.14 m

       

Hence we can conclude that The maximum amplitude of the motion for which the block does not separate from the plate is : 0.14 m.

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