A block of mass `m` is released from rest onto a spring. A having stiffness `k_A=mg//2h` as shown in figure. If the block compresses spring B through a distance h, find the:

a. stiffness of the spring B
b. equilibrium position of the block
c. maximum velocity of the block
d. maximum acceleration of the block

Answer

a. `(4mg)/(h)`; b. `h/9`; c. `4/3sqrt(2gh)`; d. `4guarr`

Explanation

a. `mg3h=1/2k_A(2h)^2+1/2k_Bh^2`

Put `k_A=(mg)/(2h)`
And solve to get `k_B=(4mg)/(h)`
b. `mg=k_A(h+x)+k_Bximpliesx=h/9`
c. Maximum velocity will be at equilibrium position.
`mg(h+h+x)=1/2mv_(max)^2+1/2k_A(h+x)^2+1/2k_Bx^2`

Solve to get `v_(max)=4/3sqrt(2gh)`
d. Maximum acceleration will be at M:
`a_(max)=(k_A2h+k_Bh-mg)/(m)=4guarr`