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:

Answer 1

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  

     $v_{max} =  A *  (2 \pi f)$

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

=>    $v_{max} =  0.25 \  m/s$