BITSAT 2024 Shift 1 Paper

To determine the time periods of vertical oscillations in different configurations of springs, we examine each setup.
Configuration (a):
The time period, Ta, is given by the formula:
Ta=2π√‌

m

k

Configuration (b):
In this setup, two identical springs are arranged in series, effectively halving the spring constant. Thus, the time period, Tb, is:
Tb=2π√‌

m

k 2

=2π√‌

2m

k

Configuration (c):
In this setup, two identical springs are arranged in parallel, effectively doubling the spring constant. Hence, the time period, Tc, is:
Tc=2π√‌

m

2k

Now, calculating the ratios of these time periods, we get:
Ta:Tb:Tc=1:√2:‌

1

√2

This ratio expresses the relative oscillation times for each configuration of the springs.