When an object of mass 357 grams is suspended from a spring, the spring is stret

Question

When an object of mass 357 grams is suspended from a spring, the spring is stretched by 20 cm. Spring constant= 17.493

2) The mass and spring are set into oscillation. What is the period of this oscillation?

3) If the amplitude of the oscillation is 17 cm, what is the maximum kinetic energy of the mass?

4) If the amplitude of the oscillation is still 17 cm, what is the maximum speed of the mass?

A 50 g mass is attached to a massless spring and allowed to oscillate around an equilibrium according to: y(t) = 1.2*sin( 3.1415*t ) where y is measured in meters and t in seconds. Amplitude=1.2

2) What is the frequency of this motion?

3) What is the period of the motion?

I'm having a hard time figuring out these parts of the two questions. I've figured out other pieces but not these.

Explanation / Answer

part 1 )

w = sqrt(k/m)

w = sqrt(17.493 N/m/.357kg)

w = 7 rad/s

we know that

w = 2pif = 2pi/T

f = w/2pi = 1.114 Hz

T = 2pi/w = 0.8976 s

Emax = 1/2 * kA^2

Emax = 1/2 * 17.493 * (0.17)^2 = 0.25277 J

Vmax = Aw = 0.17 * 7 = 1.19 m/s

part b )

y(t) = Asin(wt)

compare wit hthis equation

w = 3.1415

f = w/2pi = 1/2 = 0.5 Hz

T = 2pi/w = 2 s

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