Answer:
Time taken by the object is 0.012 s .
Explanation:
Given :
Frequency , f = 3.5 Hz .
Amplitude , A = 0.15 m .
At time t = 0 , x = 0 m.
Since , at time t = 0 , x = 0 m .
Therefore , equation of displacement is :
[tex]x=Asin(\omega t)[/tex] ...equation 1.
Here , [tex]\omega[/tex] is angular frequency and is given by :
[tex]\omega=2\pi f=22\ Hz.[/tex]
We need to find the time at which its displacement is , [tex]x = 4.00\times 10^{-2}\ m.[/tex]
Putting all these value in equation 1 we get ,
[tex]4\times 10^{-2}=0.15 \times sin(22\times t) \\\\0.27=sin(22\times t)\\\\22\times t=sin^{-1}{0.27}\\\\t=\dfrac{sin^{-1}0.27}{22}\\\\t=0.012\ s .[/tex]
Hence , this is the required solution.
