I wasnt able to do these on my own and would appreciate a good explanation, not

Question

I wasnt able to do these on my own and would appreciate a good explanation, not just an answer. This is due tonight, I am awarding 500 points for the right answers and explanations!

1) A 0.78-kg mass is hanging from a spring with spring constant 18 N/m. Then the mass is displaced from the equilibrium by 1.8 cm and let go. What is the resulting angular frequency of the oscillation?

2)An ideal massless spring is hanging vertically. When a 0.55-kg mass is attached to the spring, the spring stretches by 5 cm before reaching a new equilibrium. Then the mass is displaced by 2.5 cm from the new equlibrium. What is the frequency of the resulting oscillation?

3)An ideal massless spring is hanging vertically. When an unknown mass is attached to the spring, the spring stretches by 5.3 cm before reaching a new equilibrium. Then the mass is displaced by 1.4 cm from the new equlibrium. What is the frequency of the resulting oscillation?

Explanation / Answer

1)

W=sqrt(K/m) =sqrt(18/0.78)

W=4.8 rad/s

2)

F=Kx

and F=mg

KX=mg

K*0.05 =0.55*9.8

K=107.8 N/m

W=sqrt(K/m) =sqrt(107.8/0.55)

W=14 rad/s

f=W/2pi =14/2pi

f=2.228 Hz

3)

KX=mg

K/m =g/x =9.8/0.053 =184.9

W=sqrt(K/m) =sqrt(184.9)

W=13.6 rad/s

f=W/2pi =13.6/2pi

f=2.164 Hz

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