Motion can only stop when what? Ps it’s science

Atransverse wave is traveling on a string stretched along the horizontal x-axis. the equation for the vertical displacement y of the string is given by y = (1.8 x 10-3)cos[π(13x - 60t)], where all quantities are in si units. what is the maximum speed of a particle of the string

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

Find v(t), given acceleration a(t)=7j and initial velocity v(0)=k