Calculate the period T for one oscillation using the formula T = t/10. Then, calculate the square of the…

Question

Calculate the period T for one oscillation using the formula T = t/10. Then, calculate the square of the period, T2.

ScanSolve AI Tutor · Accepted Answer

Here's a breakdown of how to carry out the experiment described:

Set up the single spring system and perform initial measurements (Instructions i, ii, iii).
Set up the retort stand with a single spring as shown in Fig. 1(a). Suspend a mass of $m = 150$ g from the spring. Gently pull the mass downwards a small distance and release it to set it into vertical oscillation. Using a stopwatch, measure and record the total time, $t$ , for 10 complete oscillations.
Calculate the period and squared period for the initial mass (Instruction iv).
Calculate the period $T$ for one oscillation using the formula $T = \frac{t}{10}$ . Then, calculate the square of the period, $T^2$ .
Repeat measurements and calculations for additional masses (Instructions v, vi, vii).
Repeat the procedure from Step 1 and Step 2 for four other mass values: $m = 200$ g, 250 g, 300 g, and 350 g. For each mass, measure the time $t$ for 10 oscillations, then calculate its period $T = \frac{t}{10}$ and its squared period $T^2$ .
Set up the parallel spring system and perform initial measurements (Instructions viii, ix, x).
Reconfigure the apparatus by suspending two identical springs in parallel on the retort stand, as shown in Fig. 1(b). Suspend a mass of $m = 150$ g from this parallel spring system. Gently pull the mass downwards and release it to set it into vertical oscillation. Using a stopwatch, measure and record the total time, $t_0$ , for 10 complete oscillations.
Calculate the period and squared period for the initial mass in the parallel system (Instruction xi).
Calculate the period $T_0$ for one oscillation using the formula $T_0 = \frac{t_0}{10}$ . Then, calculate the square of the period, $T_0^2$ .
Repeat measurements and calculations for additional masses in the parallel system (Instructions xii, xiii, xiv).
Repeat the procedure from Step 4 and Step 5 for four other mass values: $m = 200$ g, 250 g, 300 g, and 350 g. For each mass, measure the time $t_0$ for 10 oscillations, then calculate its period $T_0 = \frac{t_0}{10}$ and its squared period $T_0^2$ .
Tabulate all experimental results (Instruction xv).
Create a table to organize all the collected data. The table should include columns for:
- Mass ( $m$ in g or kg)
- Time for 10 oscillations ( $t$ or $t_0$ in s)
- Period ( $T$ or $T_0$ in s)
- Squared period ( $T^2$ or $T_0^2$ in s $^2$ ) Ensure to clearly distinguish between the data collected for the single spring and the parallel spring system.
Plot the required graph (Instruction xvi).
Plot a graph with the mass ( $m$ ) on the vertical (y) axis and the squared period ( $T^2$ or $T_0^2$ ) on the horizontal (x) axis. Plot the data points for both the single spring experiment and the parallel spring experiment on the same graph. You should expect to see a linear relationship for both sets of data.

Calculate the period T for one oscillation using the formula T = (t)/(10). Then, calculate the square of the period, T2.

Step-by-step solution

Set up the single spring system and perform initial measurements (Instructions i, ii, iii).

Calculate the period and squared period for the initial mass (Instruction iv).

Repeat measurements and calculations for additional masses (Instructions v, vi, vii).

Set up the parallel spring system and perform initial measurements (Instructions viii, ix, x).

Calculate the period and squared period for the initial mass in the parallel system (Instruction xi).

Repeat measurements and calculations for additional masses in the parallel system (Instructions xii, xiii, xiv).

Tabulate all experimental results (Instruction xv).

Plot the required graph (Instruction xvi).

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