question_answer

The oscillation of a body on a smooth horizontal surface is represented by the equation,\[X=A\cos (\omega t)\]                                                                                                                                                                       [NEET 2014]

where    \[X=\] displacement at time t

\[\omega =\] frequency of oscillation

Which one of the following graphs shows correctly the variation a with t?

A)  

B)  

C)

D)             Here,   \[a=\] acceleration at time t \[T=\] time period

Correct Answer: A

Solution :

We can find the correct graph by putting different values of t in the given expression

\[x=A\cos (\omega t)\]

\[\Rightarrow \]   At \[t=0,x=+A\]

and \[t=\frac{T}{4},x=A\cos \left( \frac{2\pi }{T}\times \frac{T}{4} \right)=A\cos (\pi /2)=0\]

Again \[t=\frac{T}{2},x=A\cos \left( \frac{2\pi }{T}\times \frac{T}{2} \right)=A\cos \pi =-A\]

We can see that, only graph (i) will satisfy the above results