oscillations Questions

The bob of a simple pendulum executes simple harmonic motion in water with a period $t$, while the period of oscillation of the bob is $t_0$ in air. Neglecting frictional force of water and given that the density of the bob is $\frac{4}{3}\times 1000{\text{kg/m}}^3$. What relationship between $t$ and $t_0$ is true?

A particle at the end of a spring executes simple harmonic motion with a period $t_1$, while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $T$, then:

The total energy of a particle executing simple harmonic motion is:

A particle of mass $m$ is attached to a spring (of spring constant $k$) and has a natural angular frequency ${\omega }_0$. An external force $F(t)$ proportional to $\cos \omega t$ ($\omega \ne {\omega }_0$) is applied to the oscillator. The displacement of the oscillator will be proportional to:

In forced oscillation of a particle, the amplitude is maximum for a frequency ${\omega }_1$ of the force, while the energy is maximum for a frequency ${\omega }_2$ of the force, then: