T = 27, 1 - 16
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The approximation sin x ≈ x to show that
the period T of a pendulum released at an angle θ has the following second-order approximation:
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- Consider two pendulums with lengths l1 and l2 performing simple harmonic motion. Find theratio l1/l2, if it is given that the first pendulum swings back and forth 10 times per minute, and the second one swings back and forth 300 times per hour.Part 2) An organ pipe of length L = 4.6 m is open at both ends. It is driven to oscillate with a standing wave that has two nodes within the pipe. (a) What is the wavelength of the standing wave? m (b) If the speed of sound in air is 330m/s, what is the frequency that the organ pipe is oscillating at in this mode? HzFind the equation for the motion of a simple pendulum (the differential equation for θ as a function of t). Show that, for small θ, this is approximaiately a simple harmonic equation and find θ if θ = θ0, dθ/dt when t = 0.
- Show that the maximum tension in the string of a simple pendulum, when the amplitude θm is small, is mg(1+θm^2). At what position of the pendulum is the tension a maximum?Asap plzA 0.20 kg ball is tied to a string. It is pulled to an angle of 8.00º and released to swing as a pendulum. At student with a stopwatch finds that 10 oscillations take 12 s. How long is the string? Use g = 10 m/s/s.