A block attached to an ideal spring undergoes simple harmonic motion about its equilibrium position (x=0) with amplitude A .What fraction of the total energy is in the form of kinetic energy when the block is at position x =1/2A a. 1/2 b. 1/3 C. 3/8 d. 3/4

Question

A block attached to an ideal spring undergoes simple harmonic motion about its equilibrium position (x=0) with amplitude A .What fraction of the total energy is in the form of kinetic energy when the block is at position x =1/2A a. 1/2 b. 1/3 C. 3/8 d. 3/4

Answer 1

To solve this problem, we need to use the principles of simple harmonic motion (SHM) and the conservation of mechanical energy.Given information:- The block undergoes simple harmonic motion about its equilibrium position (x = 0) with amplitude A.- The position of the block is x = 1/2A.In SHM, the total mechanical energy (E) is the sum of the kinetic energy (K) and the potential energy (U) of the spring.The total mechanical energy is given by:E = (1/2)kA^2Where k is the spring constant.At the equilibrium position (x = 0), the kinetic energy is at its maximum, and the potential energy is zero.At the amplitude (x = A), the potential energy is at its maximum, and the kinetic energy is zero.The kinetic energy at a general position x is given by:K(x) = (1/2)k(A^2 - x^2)Substituting x = 1/2A, we get:K(1/2A) = (1/2)k(A^2 - (1/2A)^2)K(1/2A) = (1/2)k(A^2 - 1/4A^2)K(1/2A) = (1/2)k(3/4A^2)Now, we can find the fraction of the total energy in the form of kinetic energy when the block is at position x = 2A:Fraction of kinetic energy = K(1/2A) / EFraction of kinetic energy = [(1/2)k(3/4A^2)] / [(1/2)kA^2]Fraction of kinetic energy = 3/8Therefore, the correct answer is:c. 3/8

Вопрос

A block attached to an ideal spring undergoes simple harmonic motion about its equilibrium position (x=0) with amplitude A .What fraction of the total energy is in the form of kinetic energy when the block is at position x =1/2A a. 1/2 b. 1/3 C. 3/8 d. 3/4

Решения

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