Waves And Oscillations

Amplitude of given SHM = A
The distance moved by? the particle in one oscillation is 4A.

Frequency of the heart, = Number of beats per second Time period of the heart,

Angular frequency of spring - block system is given by

Maximum speed in oscillation


Here,

Time period of spring block system is given by,

Here, mass of block =
Spring constant

Resonance occurs when the frequency of the external force matches the natural frequency of the oscillating system. At this point, the system absorbs energy most efficiently. As energy is continually supplied at the resonant frequency, the amplitude of oscillation increases significantly. Therefore, the correct answer is (A). The frequency and time period do not change; only the amplitude becomes large.

We are given a spring with force constant that is cut into lengths in the ratio . We need to determine the relationship between the new force constant when the springs are connected in series and in parallel. Step 1: Force Constant in Series When springs are connected in series, the equivalent spring constant is given by the formula: Since the springs are cut into lengths in the ratio , the force constant of a spring is inversely proportional to its length. Hence, the force constants of the individual springs are in the ratio . The new force constant for the series combination is calculated by: Thus, So, the new force constant when connected in series is . Step 2: Force Constant in Parallel When springs are connected in parallel, the equivalent spring constant is given by: Since the springs are in the ratio , the force constants are in the ratio . Therefore, Thus, the force constant when connected in parallel is . Step 3: Ratio of to Now, we calculate the ratio of to : Thus, the ratio . Hence, the correct answer is (B) 3.38.