$A$ particle of mass $200 \,g$ executes $S.H.M.$ The restoring force is provided by a spring of force constant $80 \,N/m$. The time period of oscillations is .... $s$.

Assuming all pulleys,springs,and strings are massless. Consider all surfaces smooth. Choose the correct statement$(s)$.

$A$ $1 \, kg$ block attached to a spring vibrates with a frequency of $1 \, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8 \, kg$ block placed on the same table. The frequency of vibration of the $8 \, kg$ block is ..... $Hz$.

The total mechanical energy of a spring-mass system in simple harmonic motion is $E = \frac{1}{2}m\omega^2 A^2$. Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude $A$ remains the same. The new mechanical energy will:

Two identical springs of constant $K$ are connected in series and parallel as shown in the figure. $A$ mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillations will be

$A$ mass $M$ is suspended from a light spring. An additional mass $m$ added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period: