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P » Em the Total Mechanical Energy of a Spring-mass System in Simple Harmonic Motion is E = 1 2 M ω 2 a 2 . - Physics

MCQ

The total mechanical energy of a spring-mass system in simple harmonic motion is \[E = \frac{1}{2}m \omega^2 A^2 .\] Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will

Options

  • become 2E

  • become E/2

  • become \[\sqrt{2}E\]

  • remain E

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Solution

remain E

Mechanical energy (E) of a spring-mass system in simple harmonic motion is given by, \[E_{} = \frac{1}{2}m \omega^2 A^2\]

where m is mass of body, and \[\omega\] is angular frequency.

Let m1 be the mass of the other particle and ω1 be its angular frequency.
New angular frequency ω1 is given by,\[\omega_1 = \sqrt{\frac{k}{m_1}} = \sqrt{\frac{k}{2m}} ( m_1 = 2m)\]

New energy E1 is given as,

\[E_1 = \frac{1}{2} m_1 \omega_1^2 A^2 \]

\[ = \frac{1}{2}(2m)(\sqrt{\frac{k}{2m}} )^2 A^2 \]

\[ = \frac{1}{2}m \omega^2 A^2 = E\]

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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 12 Simple Harmonics Motion
MCQ | Q 11 | Page 251
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