
State two conditions necessary for a mass to be undergoing simple harmonic motion.
A trolley of mass
is held on a horizontal surface by means of two springs attached to fixed points P and Q, as shown in the figure below.
The springs, each having a spring constant
of
, are always extended. The trolley is displaced along the line of the springs and then released. The variation with time
of the displacement
of the trolley is shown in the graph below.
The acceleration
of the trolley of mass
may be assumed to be given by the expression

Calculate the angular frequency
of the oscillations of the trolley.
Determine the time
shown on the graph above.