A solid right circular cylinder of weight 10 kg and cross- section al area 100 cm2 is suspended by a spring, where k=11 kg/cm, and hangs partially submerged in water of density 1000 kg/m3 as shown in figure. What is its period when it makes simple harmonic vertical oscillations? (Take g=10 m/s2)

Let the cylinder be depressed a distance x metres into waterfrom the position of rest.Increase in tension of spring = 100x metres into water fromthe position of restIncrease in tension of spring = 100x kg-wtA=100cm2=10−2m2 Increase in buoyancy =1001002x×1000kg−wtK = 1 kg-wt/cm = 100 kg-wt/m = 10x kg-wtTotal unbalanced vertical force on the cylinder=100x+ 10x= 110x kg-wt Acceleration of cylinder =110x×1010m/s2=110xm/s2 Period of one oscillation =2π110=0.6s