SATHEE: Simple Harmonic Motion 3 Question 3

Simple Harmonic Motion 3 Question 3

3. A particle executes simple harmonic motion with an amplitude of $5 c m$ . When the particle is at $4 c m$ from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time (in seconds) is

(2019 Main, 10 Jan II)

(a) $\frac{4 π}{3}$

(b) $\frac{8 π}{3}$

(d) $\frac{3}{8} π$

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Answer:

Correct Answer: 3. (b)

Solution:

In simple harmonic motion, position $(x)$ , velocity $(v)$ and acceleration $(a)$ of the particle are given by

$\begin{aligned} x = A \sin ω t \\ v = ω \sqrt{A^{2} - x^{2}} or v = A ω \cos ω t \end{aligned}$

$and a = - ω^{2} x or a = - ω^{2} A \sin ω t$

Given, amplitude $A = 5 c m$ and displacement $x = 4 c m$ . At this time (when $x = 4 c m$ ), velocity and acceleration have same magnitude.

$\begin{aligned} \Rightarrow | v_{x = 4} | = | a_{x = 4} | or | ω \sqrt{5^{2} - 4^{2}} | = | - 4 ω^{2} | \\ \Rightarrow 3 ω = + 4 ω^{2} \Rightarrow ω = (3 / 4) r a d / s \end{aligned}$

So, time period, $T = \frac{2 π}{ω} \Rightarrow T = \frac{2 π}{3} \times 4 = \frac{8 π}{3} s$

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Simple Harmonic Motion 3 Question 3

3. A particle executes simple harmonic motion with an amplitude of $5 c m$ . When the particle is at $4 c m$ from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time (in seconds) is

Answer:

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Simple Harmonic Motion 3 Question 3

3. A particle executes simple harmonic motion with an amplitude of 5cm. When the particle is at 4cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time (in seconds) is

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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3. A particle executes simple harmonic motion with an amplitude of $5 c m$ . When the particle is at $4 c m$ from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time (in seconds) is