Question

An object that is oscillating on a spring is given by the equation x = (10.0 cm) cos[(6.00 s-1)t]. At what value of t after t = 0.00 s is the cart first located at x = 8.00 cm?

Answer 1

`t=0.0107\ \text{s}`

Step-by-step explanation:

`x=10\cos(6t)`

Now
`x=8\ \text{cm}`

Substituting the value of
`x` in the equation we get

`8=10\cos6t`

`\Rightarrow 0.8=\cos6t`

`\Rightarrow \cos^(-1)0.8=6t`

`\Rightarrow t=(\cos^(-1)0.8)/(6)` the values here are used found in radians

`\Rightarrow t=0.0107\ \text{s}`

So, at
`t=0.0107\ \text{s}` the value of
`x=8\ \text{cm}`.