What is the maximum velocity of a simple harmonic motion with amplitude '$a$' and time period '$T$ seconds'?

$A$ particle performs simple harmonic motion with amplitude $A$. Its speed is increased to three times at an instant when its displacement is $\frac{2A}{3}$. The new amplitude of motion is $\frac{nA}{3}$. The value of $n$ is . . . . . . .

$A$ particle is performing simple harmonic motion. Which of the following statements are correct?
$(i)$ Its velocity-displacement graph is parabolic in nature.
$(ii)$ Its velocity-time graph is sinusoidal in nature.
$(iii)$ Its velocity-acceleration graph is elliptical in nature.

$A$ body is executing $S.H.M.$ When its displacement from the mean position is $4 \, cm$ and $5 \, cm$,the corresponding velocity of the body is $10 \, cm/sec$ and $8 \, cm/sec$. Then the time period of the body is

$A$ particle executes $S.H.M.$ starting from the mean position. Its amplitude is '$a$' and its periodic time is '$T$'. At a certain instant,its speed '$u$' is half that of maximum speed $V_{\text{max}}$. The displacement of the particle at that instant is

$A$ particle of mass $2 \, kg$ executing $SHM$ has an amplitude of $20 \, cm$ and a time period of $1 \, s$. Its maximum speed is ......... $m/s$.