If a spring mass system is placed on a horizontal smooth surface. Then find the net work done by spring force after one time period(assume suitable variables)
Asked by Pjdrd24680
15th September 2018,
8:06 AM
Answered by Expert
Answer:
Let us assume the mass m is subjected to SHM due to spring force.
dispalcement x at any time t is given by, x = a sin(ωt ) .......................(1)
where a is displacement, ω is angular speed.
speed at time t is given by, 
acceleration at time t is given by, 
force F = mass× acceleration 
workdone dW for small displacement dx is given by,
dw = F×dx 
eqn.(5) is rewriteen as, 
........................(6)
........................(6)Let us substitutute θ = 2×ω×t in (6) and rewrite as, 
workdone for one time period, 
Note the limit of integration :- when t = T, θ = 2×ω×t = 2×ω×T = 4π , where T is one time period
when a sine function is integrated from 0 to 4π, i.e. two full cycles, net result is zero.
hence net workdione for a time period is zero.
Answered by Expert
17th September 2018,
12:27 PM
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