$A$ plate oscillates with a time period $T$. If another plate is suddenly placed on the first plate,what happens to the time period?

Two simple pendulums are given: the first has a bob of mass $M_1$ and length $L_1$,and the second has a bob of mass $M_2$ and length $L_2$. Given $M_1 = M_2$ and $L_1 = 2L_2$. If the vibrational energy of both is the same,which of the following statements is correct?

$A$ simple pendulum of string length $30 \ cm$ performs $20$ oscillations in $10 \ s$. The length of the string required for the pendulum to perform $40$ oscillations in the same time duration is . . . . . . $cm$. [Assume that the mass of the pendulum remains same.]

$A$ simple pendulum of length $2 \ m$ is given a horizontal push through an angular displacement of $60^{\circ}$. If the mass of the bob is $200 \ g$,the angular velocity of the bob will be (Take acceleration due to gravity $g = 10 \ m/s^2$).

In a seconds pendulum,the mass of the bob is $30\, g$. If it is replaced by a $90\, g$ mass,then its time period will be .... $s$.

$A$ simple pendulum is executing simple harmonic motion with a time period $T$. If the length of the pendulum is increased by $21\%$,the percentage increase in the time period of the pendulum of increased length is ..... $\%$