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A 0.500−kg mass is suspended from a string, forming a pendulum. The period of this pendulum is 1.74 s when the amplitude is 1.00 cm. The mass of the pendulum is now reduced to 0.250 kg. What is the period of oscillation now, when the amplitude is 2.00 cm ?

User Sublimemm
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Final answer:

The period of the new pendulum when the amplitude is 2.00 cm is approximately 1.63 seconds.

Step-by-step explanation:

The period of a pendulum is determined by its length and the gravitational acceleration. The formula to calculate the period of a pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. Let's use this formula to solve the problem. In the first scenario, the initial mass of the pendulum is 0.500 kg and the period is 1.74 s. The amplitude is not relevant for calculating the period. We can plug these values into the formula to find the length of the pendulum. T = 2π√(L/g) 1.74 = 2π√(L/9.8) Now, we can solve for L: L = (1.74/2π)^2 * 9.8 Next, we can calculate the length of the new pendulum when the mass is reduced to 0.250 kg. By rearranging the formula, we can solve for the new period: T' = 2π√(L'/g) 2.00 = 2π√(L'/9.8) Solving for L', we find: L' = (2.00/2π)^2 * 9.8 Therefore, the period of oscillation of the new pendulum when the amplitude is 2.00 cm is approximately 1.63 seconds.

User Jvatic
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