Question

A solid ball of mass m is made to fall from a hieght H on a pan suspended through a spring constant K.if the ball does not rebound and the pan is massless theb amplitude of oscillation is.

Answer 1

force due to gravity on the ball= mg= force exerted by ball on spring.
force exterted by spring to the ball mass m= -kX
hence by Newton's third law
mg= kX
Now
potential energy(P.E) of the ball to Amptlitude A is
= mg(H+X+A)
kinetic energy (K.E) of spring = -1/2{k(X+A)^2}
from law of conservation of energy
k.E+P.E= 0
hence
K.E= P.E
1/2{k(X+A)^2} = mg(H+X+A)
mgH +mgx + mgA= ½ kA^2 +kxA + ½ kx^2
we know mg =kX, replace kX by mg
mgH +mg(mg/k)+mgA = ½ kA^2 + mgA + ½ k(mg/k)^2

mgH +(mg)^2/k = ½kA^2 +½(mg)^2/k

½ kA^2 = mgH +½ (mg)^2/k

A = square root of [ 2mgH/k + (mg/k)^2]

Answer 2

above answer is correct