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My Attempt:

total energy of the mass moving with amplitude A and oscillating with frequency f will be

E = mA^2ω^2 / 2

where ω = 2πf

f = frequancy of oscillation

A = amplitude of oscillation .

at the mean postion the total eneregy will be in kinetic energy form

E = mv^2 / 2

v =velocity of the mass at equalibrium

if 0.5m/sec is added to velocity

Now the new total eneryg

E' = m*(v + 0.5)^2 / 2 .

m = mass of the block

E' = mA'^2 ω^2 / 2

the frequancy remains constanat

and the amplidue to of the new oscillation changes

ω = 2E' / mA'^2

but at the end I am left with 2 unknown and i am not to solve this

please help its urgent