Setup for a single spring system.

Suspend a single spring from a retort stand using a clamp, as shown in Fig. 1(a). Attach a mass $m = 150 \, \text{g}$ to the free end of the spring. Gently pull the mass downwards and release it to set it into vertical oscillation.

Using a stopwatch, measure the time $t$ for 10 complete oscillations of the mass. Record this time $t$. Calculate the period $T$ of oscillation using the formula:

Then, calculate the square of the period, $T^2$.

Repeat Step 1 and Step 2 for four other values of mass: $m = 200 \, \text{g}, 250 \, \text{g}, 300 \, \text{g}$, and $350 \, \text{g}$. For each mass, record the time $t$ for 10 complete oscillations and calculate the corresponding $T$ and $T^2$ values.

With the aid of screws, suspend two identical springs in parallel from the retort stand, as shown in Fig. 1(b). Attach a mass $m = 150 \, \text{g}$ to the combined spring system. Gently pull the mass downwards and release it to set it into vertical oscillation.

Using a stopwatch, measure the time $t_0$ for 10 complete oscillations of the mass. Record this time $t_0$. Calculate the period $T_0$ of oscillation using the formula:

Then, calculate the square of the period, $T_0^2$.

Repeat Step 4 and Step 5 for four other values of mass: $m = 200 \, \text{g}, 250 \, \text{g}, 300 \, \text{g}$, and $350 \, \text{g}$. For each mass, record the time $t_0$ for 10 complete oscillations and calculate the corresponding $T_0$ and $T_0^2$ values.

Create a table to record all the collected data and calculated values. The table should include columns for:

• Mass $m \, (\text{g})$
• Time $t$ for 10 oscillations (single spring) $(\text{s})$
• Period $T$ (single spring) $(\text{s})$
• $T^2$ (single spring) $(\text{s}^2)$
• Time $t_0$ for 10 oscillations (two springs) $(\text{s})$
• Period $T_0$ (two springs) $(\text{s})$
• $T_0^2$ (two springs) $(\text{s}^2)$

Plot a graph with mass $m$ (in grams) on the vertical axis and $T^2$ (in seconds squared) on the horizontal axis. Plot two sets of points on the same graph: one for the single spring system ($m$ vs $T^2$) and another for the two-spring system ($m$ vs $T_0^2$). Draw the best-fit line for each set of points.