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`

Step-by-step 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 =  (1)/(T)`

=>
`f =  (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`