IIT JEE Advanced 2009 Paper 1

The equation of single harmonic motion is x = A sin (

2π

T

t), where A is amplitude and T is the time period of the motion.
From the given figure, A = 1 and T = 8. Thus,
x = sin (

π

4

t)
x = sin (

π

t

)
The acceleration is
a =

d2x

dt2

= −

π2

1

sin(

π

4

t)
At time t =

4

3

s , the acceleration is
a = −

π2

16

sin(

π

4

×

4

3

) = -

√3

32

π2‌cm∕s2