SATHEE: Oscillations - Result Question 63

Oscillations - Result Question 63

69. A particle, with restoring force proportional to displacement and resistve force proportional to velocity is subjected to a force $F \sin ω_{0}$ . If the amplitude of the particle is maximum for $ω = ω_{1}$ and the energy of the particle is maximum for $ω = ω_{2}$ , then

(a) $ω_{1} = ω_{0}$ and $ω_{2} \neq ω_{0}$

(b) $ω_{1} = ω_{0}$ and $ω_{2} = ω_{0}$

[1989]

(d) $ω_{1} \neq ω_{0}$ and $ω_{2} \neq ω_{0}$

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Solution:

(c) At maximum energy of the particle, velocity resonance takes place, which occurs when frequency of external periodic force is equal to natural frequency of undamped vibrations, i.e. $ω_{2} = ω_{0}$ .

Further, amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped natural vibrations, i.e., $ω_{1} \neq ω_{0}$ .

Oscillations - Result Question 63

69. A particle, with restoring force proportional to displacement and resistve force proportional to velocity is subjected to a force $F \sin ω_{0}$ . If the amplitude of the particle is maximum for $ω = ω_{1}$ and the energy of the particle is maximum for $ω = ω_{2}$ , then

Solution:

14

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Oscillations - Result Question 63

69. A particle, with restoring force proportional to displacement and resistve force proportional to velocity is subjected to a force Fsin⁡ω0. If the amplitude of the particle is maximum for ω=ω1 and the energy of the particle is maximum for ω=ω2, then

Solution:

14

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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69. A particle, with restoring force proportional to displacement and resistve force proportional to velocity is subjected to a force $F \sin ω_{0}$ . If the amplitude of the particle is maximum for $ω = ω_{1}$ and the energy of the particle is maximum for $ω = ω_{2}$ , then