a) Show that the total energy of a simple pendulum undergoing oscillations of small amplitude theta...
a) Show that the total energy of a simple pendulum undergoing oscillations of small amplitude theta in radians, is E=0.5m*g*L*theta. Use the approximation cos theta=1-0.5*theta^2 for small theta
b) Using the conservation of energy, find an expression for its speed as it passes through theta=0
Homework Answers
you have mentioned
0.5m*g*l*theta but its 0.5 m*g*l*theta^2Add Answer to:
a) Show that the total energy of a simple pendulum undergoing
oscillations of small amplitude theta...
A mass at the end of a spring is undergoing simple harmonic oscillations with amplitude A....
A mass at the end of a spring is undergoing simple harmonic oscillations with amplitude A. a) What fraction of the total mechanical energy is kinetic if the displacement is ⅓ the amplitude? a) In terms of A, find the value of displacement x at which the potential energy equals 1 /16 of the total mechanical energy.
A simple pendulum on the surface of Earth is found to undergo 11.0 complete small-amplitude oscillations...
A simple pendulum on the surface of Earth is found to undergo 11.0 complete small-amplitude oscillations in 8.55 s. Find the pendulum's length. length of the pendulum: .00156 m
A pendulum consists of a string of length L and a mass m hung at one...
A pendulum consists of a string of length L and a mass m hung at one end and the mass oscillates along a circular arc. Part a) Familiarize yourself with the derivation of omega = Squareroot g/L to hold. i) Explain succinctly how the angular frequency of oscillation omega = Squareroot g/L comes about from Newton's Law, where g is the gravitational acceleration. ii) One assumption required is the small angle approximation: sin theta = theta and cos theta =...
A certain simple pendulum consists of a small 750.0 ? bob that swings on the end...
A certain simple pendulum consists of a small 750.0 ? bob that swings on the end of a 25.0 ?? string. The small amplitude of the oscillations of this pendulum decays to half its original value after 45.0 oscillations. The angular position of the pendulum as a function of time, ?(?), can be expressed as follows. ?(?) = ??0 ? − ??/2m cos(? ′ ? + ?) ??0 is the original angular amplitude. ? is the time, and ? is...
The length of a simple pendulum undergoing SHM is 2.0 m. If the amplitude is 15...
The length of a simple pendulum undergoing SHM is 2.0 m. If the amplitude is 15 degrees, what is the gravitational potential energy of the pendulum's bob if it has a mass of 0.100 kg? How fast does the pendulum's bob pass through the equilibrium position?
A mass m at the end of a spring of spring constant k is undergoing simple harmonic oscillations with amplitude A.
A mass m at the end of a spring of spring constant k is undergoing simple harmonic oscillations with amplitude A. Part (a) At what positive value of displacement x in terms of A is the potential energy 1/9 of the total mechanical energy? Part (b) What fraction of the total mechanical energy is kinetic if the displacement is 1/2 the amplitude? Part (c) By what factor does the maximum kinetic energy change if the amplitude is increased by a factor of 3?
Consider a pendulum of length l and a bob of mass m at its end, moving...
Consider a pendulum of length l and a bob of mass m at its end, moving through oil with theta decreasing. The massive bob undergoes small oscillations, but the oil retards the bob's motion with a resistive force proportional to the speed with Fres=2m(sqrt(g/ l))*(l(theta)).The bob is initially pulled back at t=0 with theta=alpha and (theta)'=0. Find the angular displacement theta and velocity theta' as a function of time.
The period T of a simple pendulum with small oscillations is calculated from the formula T=2pi sqrt(L/g) where L is the...
The period T of a simple pendulum with small oscillations is calculated from the formula T=2pi sqrt(L/g) where L is the length of the pendulum and g is the acceleration due to gravity. suppose that measured values of L and g have errors and are corrected with new values where L is increased from 4m to 4.5m and g is increased from 9 m/s2 to 9.8 m/s2. Use differentials to estimate the change in the period. Does the period increase...
2. The position of the motion of the bob in a simple pendulum in radians is...
2. The position of the motion of the bob in a simple pendulum in radians is given by 0(t)-3cos What is the amplitude, frequency, and period of the motion? 3.A man enters a tall tower needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor, and its period is 12 s. How tall is the tower? Two playground swings start out together. After 5 complete oscillations, the swings are out of...
#2 by schedule: The Simple Pendulum 1. The swing angle of the pendulum is "small" when...
#2 by schedule: The Simple Pendulum 1. The swing angle of the pendulum is "small" when the period following from the fll analysis (Eq.(2) in the text) differs from the period obtained using the truncated formula, Eq.(1) at most by 0.5%. If we consider the summation in Eq.(2) only up to the second term, calculate this angle in radians, and convert it to arc degrees. (L/g)1/ T const. X (1) A fuller analysis of the problem provides a solution for...
A simple pendulum on the surface of Earth is found to undergo 11.0 complete small-amplitude oscillations in 8.55 s. Find the pendulum's length. length of the pendulum: .00156 m
A pendulum consists of a string of length L and a mass m hung at one end and the mass oscillates along a circular arc. Part a) Familiarize yourself with the derivation of omega = Squareroot g/L to hold. i) Explain succinctly how the angular frequency of oscillation omega = Squareroot g/L comes about from Newton's Law, where g is the gravitational acceleration. ii) One assumption required is the small angle approximation: sin theta = theta and cos theta =...
2. The position of the motion of the bob in a simple pendulum in radians is given by 0(t)-3cos What is the amplitude, frequency, and period of the motion? 3.A man enters a tall tower needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor, and its period is 12 s. How tall is the tower? Two playground swings start out together. After 5 complete oscillations, the swings are out of...
#2 by schedule: The Simple Pendulum 1. The swing angle of the pendulum is "small" when the period following from the fll analysis (Eq.(2) in the text) differs from the period obtained using the truncated formula, Eq.(1) at most by 0.5%. If we consider the summation in Eq.(2) only up to the second term, calculate this angle in radians, and convert it to arc degrees. (L/g)1/ T const. X (1) A fuller analysis of the problem provides a solution for...
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