Question

Does anyone know the answer to the question below.

Answer 1

The correct answer is -

option A)

Explanation:

It is given that the maximum of the wave is 100 units

For option A)

F(t) would be maximum when cos(
`(2π)/(5)`t) = -1

∴
`F(t)_(max)` = 60 - 40(-1) = 60 + 40 = 100

Similarly we get ,

`F(t)_(max)` = 100 for all other options.

Also It is given that minimum of the wave is 20 units.

For option a)

Minimum of F(t) occurs when

cos(
`(2π)/(5)`t) = 1

∴
`F(t)_(min)` = 60 - 40 = 20.

However for option B) and D) , in a similar manner -

`F(t)_(min)` = - 60

But for option C)

`F(t)_(min)` = 60 + 40(-1) = 20.

Hence we discard option b) and d).

Given that the time period of the cycle is 5 ms

We know that Time period of wave is given by -

T =
`(2π)/(ω)` , where ω = angular frequency of the wave.

∴
`(2π)/(ω)` = 5.

∴ ω =
`(2π)/(5)`.

For option c)

ω = 5.

But for option a)

ω =
`(2π)/(5)`.

∵ option a) satisfies all the given conditions ,

The correct answer is option a).