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Answer :
The spring constant 'k' can be calculated using the formula k = (4π²m) / T², where m is the mass and T is the full oscillation period. Given the half oscillation period of 0.80s, the full period is 1.60s and the mass is 2.00 x 10&sup5; kg.
To find the spring constant of the spring supporting the platform, we can use the formula for the period of a mass-spring system in simple harmonic motion, T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. Given that the period (the time to oscillate from the top to the bottom positions and back to the top) is 0.80 s for one half oscillation, the full period is 1.60 s. Hence, we can rearrange the formula to solve for k:
k = (4π²m) / T²
Plugging in the values, we have:
k = (4π² × 2.00 × 10&sup5; kg) / (1.60 s)²
Thus, we can calculate the spring constant k for the given mass and oscillation period.
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