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1.18. A particle P of mass m can slide without friction on a rigid fixed wire. It is connected to a fixed point o through a linear damper with a damping coefficient c. Assuming the initial conditions x(0) = 0, (0) = vo, solve for the initial velocity vo which will cause the particle to stop at x = h. Figure P 1.18.
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Answers Given that 1.1.9 D A particle Can Slia p of mass m earticle p of mass m Can slide without friction on vid fixed wire. it is connected to a fined point o through a lineas damper with a damping coefficient ce tions xo)=0, (o)= Vo, sove • Assuming the for the initial velocity to which will cause the particle to stop ata=h. Now, a lineas dampar, particle of mass In this problem, we are considering which means the camping force on the m is, I Fad ay = Ed=-cu C hitalen Where is damping Cocllicient since this force is applied on the body at an angle o. only a component force will be acting on as shown below. the mass Fasino Fa cose

mass is moving from B to A So, we have to . Consider the damping force acting from A to B Copposite to molion) Therefore, damping force on the body sy been fartfd isino -0. of where fd = - cu & sin o > Alle , sino = 2 2 2 from Newton's second law, any force ruth? link Fama am. de Em Vide substituting these leawes in ☺ du = en 12 thels de tzo, initially the body is at n=0 with Velocity vo and when ask the body stupes, ie, co s Therefore, Integrating with these limits usiv - Share on

To find the integral in the RHS go for subetta put u=nth? (where onlyn is the variable) du - 27-dx wide = du this limits also changes as n=0 ) haoth? ah nch a nehlth2=2h2 Therefore, ancoral becomes zh ما 2 m Savu - Free to the Cubicone [onen Co-Wol e [-en lau? ) – en [h]] Vo = te om en (2) renda due = ena hans To = q to enla) ] This should be th possible initial velocity of the mass to be stopped after travelling a distance hi