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Home / Doubts and Solutions/NEET/Physics

a body is executing SHM. When the displacement from the mean position are 4cm and 5cm respectively, the magnitude of the corresponding velocity of the body are 10cms to the power of negative 1 end exponent and 8cms to the power of negative 1 end exponent. The time period of the body is

Asked by vvelesha 13th September 2018, 6:39 PM
Answered by Expert
Answer:
Equation for dispalcement 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 are two instants , so that the 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 .
 
then we have,   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)
 
By squaring and adding (3) and (4), 16+(100/ω2) = A2 ...................(7)
By squaring and adding (5) and (6), 25+(64/ω2) = A2 ...................(8)
 
By equating (7) and (8), we get, 16+(100/ω2) = 25+(64/ω2) ..........(9)
 
from (9), we get ω = 2 or (2π/T) = 2  or T = π sec
 
T is time period of SHM
Answered by Expert 14th September 2018, 11:39 AM
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