Question

A body is executing s.H.M. When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocity of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is​

Answer 1

Answer:

3.14

Explanation:

Equation for displacement x of SHM is given by  x = A × sin( ωt ) (1)

Equation for velocity dx/dt of SHM is given by  dx/dt = A×ω cos( ωt ) (2)

Let time t1 and t2 be two instants, such as respective displacements are 4 cm and 5 cm. Similarly at time t1 and t2, let the respective velocities are 10 cm/s   and 8 cm/s .

Thus,

4 = A×sin( ω t1 ) (3)

10 = A×ω×cos( ω t1 ) (4)  

5 = A×sin( ω t2 ) (5)

8 = A×ω×cos( ω t2 ) (6)

On squaring and adding (3) and (4), 16+(100/ω2) = A2 (7)

On squaring and adding (5) and (6), 25+(64/ω2) = A2  (8)

On equating (7) and (8) -

16+(100/ω2)

= 25+(64/ω2) ..........(9)

From (9), we get ω = 2 or (2π/T) = 2

or T = π sec

Thus T = 3.14

Answer 2

Answer:

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