Asimple harmonic oscillator consists of a 0.96 kg block attached to a spring (k = 220 n/m). the block slides on a horizontal frictionless surface about the equilibrium point x = 0 with a total mechanical energy of 3.0 j. (a) what is the amplitude of the oscillation? (b) how many oscillations does the block complete in 12 s? enter the integer number of complete cycles. (c) what is the maximum kinetic energy attained by the block? (d) what is the speed of the block at x = 0.12 m?

a)  

b) 29

c)

d)

Explanation:

mass, m =0.96 g

k = 220 N/m

Total energy, E = 3.0 J

Now,

a)

where, A is the amplitude

on substituting the values, we get

or

or

or

b) Time period (T) is given as:

on substituting the values,we get

or

thus, number of oscillations (N) in 12s will be

c)Maximum K.E = total mechanical energy

thus,

d)The angular frequency (ω) is given as:

on substituting the values,we get

or

Now, the speed (V) in SHM is calculated as;

for x = 0.12m

we get

or

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