Aparticle moving in simple harmonic motion with a period t = 1.5 s passes through the equilibrium point at time t0 = 0 with a velocity of 1.00 m/s to the right. a time t later, the particle is observed to move to the left with a velocity of 0.50 m/s. (note the change in direction of the velocity.) the smallest possible value of the time t is

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 710 n/m. it is initially at rest on an inclined plane that is at an angle of θ = 23° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.19. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. a) what is the block's initial mechanical energy? b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

Agas initially at p1 = 1 bar and occupying a volume of 0.5 liter is compressed within a piston–cylinder assembly to a final pressure p2 = 4 bar. (a) if the relationship between pressure and volume during the compression is pv = constant, determine the volume, in liters, at a pressure of 3 bar. (b) repeat for a linear pressure–volume relationship between the same end states. reference

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