SATHEE: Oscillations - Result Question 58

Oscillations - Result Question 58

63. A body is executing S.H.M. When the displacements from the mean position are $4 c m$ and $5 c m$ , the corresponding velocities of the body are $10 c m$ per sec and $8 c m$ per sec. Then the time period of the body is

[1991]

(a) $2 π s e c$

(b) $π / 2 s e c$

(d) $(3 π / 2) s e c$

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Solution:

$v = ω \sqrt{a^{2} - x^{2}}$ at displacement $x$ .

$\Rightarrow 10 = ω \sqrt{a^{2} - 16}$

and $8 = ω \sqrt{a^{2} - 25}$

Dividing, $\frac{5^{2}}{4^{2}} = \frac{a^{2} - 16}{a^{2} - 25} = \frac{25}{16}$

or, $16 a^{2} - 256 = 25 a^{2} - 625 \Rightarrow 9 a^{2} = 369$ $∴ a^{2} = \frac{369}{9}$

Putting this value in equation (2) mentioned above,

$10 = ω \sqrt{\frac{369}{9} - 16} \Rightarrow 10 = ω \sqrt{\frac{225}{9}}$

or, $ω = \frac{10 \times 3}{15} = 2 r a d i a n / s e c$ .

Time period $= \frac{2 π}{ω} = \frac{2 π}{2} = π s e c$ .

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Oscillations - Result Question 58

63. A body is executing S.H.M. When the displacements from the mean position are 4cm and 5cm, the corresponding velocities of the body are 10cm per sec and 8cm per sec. Then the time period of the body is

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63. A body is executing S.H.M. When the displacements from the mean position are $4 c m$ and $5 c m$ , the corresponding velocities of the body are $10 c m$ per sec and $8 c m$ per sec. Then the time period of the body is