question_answer

The oscillation of a body on a smooth horizontal surface is represented by the equation, \[X=A\cos (\omega t)\] where X = displacement at time t, \[\omega \] = frequency of oscillation. Which one of the following graphs shows correctly the variation a with t? Note:- Here, a = acceleration at time t, T = time period [AIPMT 2014]

A)  

B)  

C)   

D)  

Correct Answer: A

Solution :

We can find the correct graph by putting different values of t in the given expression \[x=A\cos (\omega t)\] 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