Can a Phase Constant Be Determined from Given Oscillation Data?

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    Oscillating Spring
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The discussion revolves around calculating the force constant (k), total energy, and position equation (x(t)) for a 3kg object oscillating on a spring with a 10 cm amplitude and 2 Hz frequency. The force constant was calculated using the formula k = (4π^2)(m)/T^2, yielding a value of approximately 473.74 N/m. For total energy, there was confusion about whether to use amplitude or another value for x in the energy equation. The position equation was correctly formulated as x(t) = 0.01sin(4π t + φ). The possibility of determining the phase constant from the given data was questioned but remains unresolved.
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Homework Statement


A 3kg object is attached to a spring and oscillates with an amplitude of 10 cm and frequency f = 2 Hz

a.) What is the force constant k of the spring?
b.) what is the total energy of this motion?
c.) Write an equation for x(t) describing the position of this object relative to its equilibrium position. Can phase constant be determined from the information given?[/B]

Homework Equations


k = (4π^2)(m)/T^2
TE= 1/2kx^2+1/2mv^2
1/2kA^2 = 1/2kx^2+1/2mv^2[/B]

The Attempt at a Solution



a.) k = 4π^2(3)/(0.5)^2 = 473.74
b.) First I attempted to find the velocity from the equation 1/2kA^2 = 1/2kx^2+1/2mv^2 I have trouble putting something in for x. Should I just put the amplitude in for x?
c.) x(t) = 0.01sin(4π t + φ) [/B]
 
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Welcome to PF!

Parts (a) and (c) look good except that you have not included units. Do you need to worry about significant figures?

Hint for (b): Does it matter at which point of the motion you calculate the energy?
 
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TSny said:
Welcome to PF!

Parts (a) and (c) look good except that you have not included units. Do you need to worry about significant figures?

Hint for (b): Does it matter at which point of the motion you calculate the energy?
Thank you!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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