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Lina20 [59]
4 years ago
12

A boy throws a ball on a spring scales which oscillates about the equilibrium position with a period of T = 0.5 sec. The amplitu

de of the vibration is A = 2 cm. Assume the ball does not bounce from the scales’s surface afterwards. Assume the vibration of the scale is expressed mathematically as x(t) = Acos(t + ). Find:
Physics
1 answer:
liq [111]4 years ago
6 0

Complete Question

A boy throws a ball on a spring scales which oscillates about the equilibrium position with a period of T = 0.5 sec. The amplitude of the vibration is A = 2 cm. Assume the ball does not bounce from the scales’s surface afterwards. Assume the vibration of the scale is expressed mathematically as x(t) = Acos(t + ). Find:

a) frequency

b) the maximum acceleration

c) the maximum velocity

Answer:

a

f =  2  \ Hz

b

a_{max} =  3.2 \ m/s^2

c

v_{max} =  0.25 \  m/s

Explanation:

From the question we are told that

   The period is  T  =  0.5 \ sec

    The  amplitude is  A =  2 \ cm  =  0.02 \ m

    The  vibration of the scale is  Acos(wt +  \phi )

Generally the frequency is mathematically represented as

   f =  \frac{1}{T}

=>   f =  \frac{1}{0.5}

=>    f =  2  \ Hz

The  maximum acceleration is mathematically represented as

    a_{max} =  A *(2 \pi f)^2

=>    0.02 *  (2 * 3.142  *  2)^2

=>  a_{max} =  3.2 \ m/s^2

The  maximum velocity is mathematically represented as  

     v_{max} =  A *  (2 \pi f)

=>    v_{max} =  0.02 *  (2 * 3.142 *  2)

=>    v_{max} =  0.25 \  m/s

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Explanation:

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Answer:

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