A spring with one end attached to a mass and the other to a rigid support is stretched and released. a) magnitude of acceleration, when just released is maximum b) magnitude of acceleration, when at equilibrium position is maximum c) speed is maximum when mass is at equilibrium position d) magnitude of displacement is always maximum whenever speed is minimum
Option (a, c) are correct. Consider a spring of spring constant k is attached to mass m at one end and another end is fixed at right support. Spring is lying on a frictionless table. Now spring is stretched by a force F by x displacement then F = -kx (-) sign shows that displacement x is opposite to the direction of force applied, when a force F acts on spring, spring also applies equally to opposite force. P.E. at A21kx2 the restoring force is directly proportional to the x so execute Simple Harmonic Motion (SHM) ∴α=m−F a=m−kx At x=0; a=0 At x=x; a=m−kx So, Magnitude of a is maximum at x when released. It verifies the option (a). At the mean position where P.E. is converted into KE=21mv2. So the speed of mass is maximum at x=0. Hence, It verifies the option (c). Magnitude of a=0 at x=0; So (b) is incorrect when the mass (m) is at its maximum displacement then it returns at this point its speed may or may not be zero.
