A mass of 400 g is connected to a massless spring of force constant 10.0 N/m and is made to oscillate on a frictionless horizontal table. The mass is displaced 10 cm from the equilibrium position and released from rest. (i) What is the period of oscillations ? (ii) Find the maximum speed of the mass (iii) What is the maximum acceleration of the mass ? and (iv) what is the total energy of the mass ? [See Fig ]

Explanation

`m = 0.400 kg , k = 10.0N//m = , a = 0.10 m`
Period of oscillation `T=2pisqrt(m/k)`
`T = 2xx3.14 sqrt((0.400)/(10.00))=1.256s`
Maximum speed `=v_(max)=omegaa=(2pi)/Ta`
`= (2xx3.14)/(1.256)xx0.10`
`= 0.5 m//s`
Maximum accelerations `= aomega^2`
`0.10 xx(4xx3.14^2)/(1.256^2)`
`= 2.5 m//s^2`
Total energy `=1/2 ka^2`
`=1/2 xx10.0 xx0.10^2 =0.50J`