SATHEE: Oscillations - Result Question 1

Oscillations - Result Question 1

1. The phase difference between displacement and acceleration of a particle in a simple harmonic motion is :

[2020]

(a) $\frac{3 π}{2} r a d$

(b) $\frac{π}{2} r a d$

(d) $π r a d$

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Solution:

(d) Displacement equation of a SHM

$y = A \sin (ω t + ϕ)$

$∴$ Velocity, $v = \frac{d y}{d t} = A ω \cos (ω t + ϕ)$

Acceleration, $a = \frac{d v}{d t}$

$or, a = - A ω^{2} \sin (ω t + ϕ)$

$∴ a = A ω^{2} \sin (ω t + ϕ + π)$

Hence, phase difference between displacement and acceleration is $π$ .

2 .

(d) Att $= 0, y = 3$ , which is maximum displacement so equation will be cosine function.

$\begin{aligned} ω = \frac{2 π}{T} = \frac{2 π}{4} = \frac{π}{2} r a d / s (∵ T = 4 s) \\ y = a \cos ω t \Rightarrow y = 3 \cos \frac{π}{2} t \end{aligned}$

Oscillations - Result Question 1

1. The phase difference between displacement and acceleration of a particle in a simple harmonic motion is :

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

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Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Oscillations - Result Question 1

1. The phase difference between displacement and acceleration of a particle in a simple harmonic motion is :

Solution:

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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