$A$ body is in simple harmonic motion with a time period of $0.5 \ s$ and an amplitude of $1 \ cm$. Find the average velocity in the interval in which it moves from the equilibrium position to half of its amplitude (in $cm/s$).

$A$ particle is executing $S.H.M.$ with time period $T$. Starting from the mean position,the time taken by it to complete $\frac{5}{8}$ oscillations is ..........

$A$ particle executes a simple harmonic motion of time period $T$. Find the time taken by the particle to go directly from its mean position to half the amplitude.

$A$ particle executing a simple harmonic motion has a period of $6 \,s$. The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is

$A$ shooting game involves using a gun that fires by itself at random times. The player can only point the gun in a fixed direction while the target moves from side to side with simple harmonic motion,as shown. At which of the given regions should the player aim in order to score the greatest number of hits?

$A$ particle performing linear $S.H.M.$ has a period of $8 \ s$. At time $t=0$,it is at the mean position. The ratio of the distances travelled by the particle in the $1^{st}$ and $2^{nd}$ second is $(\cos 45^{\circ} = 1/\sqrt{2})$.