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A body of mass 20g performs a simple harmonic motion at a frequency of 5 hertz its velocity is 200cm/s calculate its maximum displacement from the main position b)maximum velocity c)maximum potential energy
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A body of mass 20g performs a simple harmonic motion at a frequency of...
Answer
Given
- Mass of the body (m) = 20 g = 0.02 kg
- Frequency (f) = 5 Hz
- Velocity (v) = 200 cm/s
Calculations
Maximum Displacement (A)
The maximum displacement of the body can be calculated using the formula:
A = v / (2πf)
Substituting the given values, we get:
A = 200 / (2 x 3.14 x 5) = 2.54 cm
Maximum Velocity
The maximum velocity of the body can be calculated using the formula:
v_max = A x 2πf
Substituting the given values, we get:
v_max = 2.54 x 2 x 3.14 x 5 = 79.6 cm/s
Maximum Potential Energy (U)
The maximum potential energy of the body can be calculated using the formula:
U_max = 0.5 x m x (2πf x A)^2
Substituting the given values, we get:
U_max = 0.5 x 0.02 x (2 x 3.14 x 5 x 2.54)^2 = 0.64 J
Explanation
Simple harmonic motion is a type of periodic motion in which the restoring force is directly proportional to the displacement from equilibrium position and acts in the opposite direction to the displacement. The motion of a body undergoing simple harmonic motion can be described by its amplitude, frequency, velocity, and potential energy. In this problem, we have been given the frequency and velocity of the body and have been asked to calculate its maximum displacement, maximum velocity, and maximum potential energy.
The maximum displacement of the body is the distance between the equilibrium position and the farthest point the body reaches in its motion. It can be calculated using the formula A = v / (2πf), where v is the velocity of the body and f is its frequency.
The maximum velocity of the body is the speed at which it moves when it reaches the maximum displacement. It can be calculated using the formula v_max = A x 2πf, where A is the maximum displacement of the body and f is its frequency.
The maximum potential energy of the body is the energy stored in the body when it is at its maximum displacement. It can be calculated using the formula U_max = 0.5 x m x (2πf x A)^2, where m is the mass of the body, A is its maximum displacement, and f is its frequency.
Thus, by using the given formulas and substituting the given values, we can calculate the maximum displacement, maximum velocity, and maximum potential energy of the body.
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A body of mass 20g performs a simple harmonic motion at a frequency of...
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A body of mass 20g performs a simple harmonic motion at a frequency of 5 hertz its velocity is 200cm/s calculate its maximum displacement from the main position b)maximum velocity c)maximum potential energy?
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A body of mass 20g performs a simple harmonic motion at a frequency of 5 hertz its velocity is 200cm/s calculate its maximum displacement from the main position b)maximum velocity c)maximum potential energy? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about A body of mass 20g performs a simple harmonic motion at a frequency of 5 hertz its velocity is 200cm/s calculate its maximum displacement from the main position b)maximum velocity c)maximum potential energy? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 20g performs a simple harmonic motion at a frequency of 5 hertz its velocity is 200cm/s calculate its maximum displacement from the main position b)maximum velocity c)maximum potential energy?.
A body of mass 20g performs a simple harmonic motion at a frequency of 5 hertz its velocity is 200cm/s calculate its maximum displacement from the main position b)maximum velocity c)maximum potential energy? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about A body of mass 20g performs a simple harmonic motion at a frequency of 5 hertz its velocity is 200cm/s calculate its maximum displacement from the main position b)maximum velocity c)maximum potential energy? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 20g performs a simple harmonic motion at a frequency of 5 hertz its velocity is 200cm/s calculate its maximum displacement from the main position b)maximum velocity c)maximum potential energy?.
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