Final answer:
The period of a pendulum with a length of 525 cm and released from rest at a starting angle of θ = 0.7 is approximately 4.6037 seconds, using the formula T = 2π √(L/g). However, this is an approximation because the starting angle is not small.
Step-by-step explanation:
To find the period of a pendulum's motion with a length of 525 cm and starting angle θ = 0.7, we use the formula for the period of a simple pendulum, which is T = 2π √(L/g). Here, L is the length of the pendulum and g is the acceleration due to gravity which is approximately 9.81 m/s². First, we need to convert the length from centimeters to meters by dividing by 100. Thus, L = 5.25 m. Plugging the length into the formula, we get T = 2π √(5.25/9.81).
Performing the calculation:
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- L = 525 cm / 100 = 5.25 m
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- T = 2π √(5.25 m / 9.81 m/s²)
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- T ≈ 2π √(0.5354)
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- T ≈ 2π (0.7319)
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- T ≈ 4.6037 seconds
However, please note that this formula assumes the amplitude of oscillation is small. A starting angle of θ = 0.7 radians is not considered small, since the small angle approximation is typically valid for angles less than about 0.1 radians. Hence, the derived period is an approximation unless θ is small.