Oscillations, velocity, elasticity

AI Thread Summary
To find the velocity of a 0.2 kg object in simple harmonic motion at a displacement of 0.04 m, the correct approach involves using the position equation x = A*cos(w*t), where A is the amplitude and w is the angular frequency calculated as w = sqrt(k/m). The user initially attempted to calculate velocity incorrectly, leading to confusion. The correct method requires determining the time when the displacement is 0.04 m and then using the velocity formula v = dx/dt = -A*w*sin(w*t) to find the instantaneous velocity. This approach will yield the expected answer of 40 cm/s.
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Homework Statement


A 0.2 kg object, suspended from a spring with a spring constant of k = 10 N/m, is moving in simple harmonic motion and has an amplitude of 0.08 m. What is its velocity at the instant when its displacement is 0.04 m?


Homework Equations


v=root(F/m/l)



The Attempt at a Solution


i did v=root(9.8*.2/.2/.04) and this gave me 15.65, but the answer is 40 cm. how? please help; i do not understand this at all. also, can you please help on thsi question? i feel stupid.
https://www.physicsforums.com/showthread.php?p=3127238#post3127238
 
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For a vibrating spring-mass system the position equation is x=A*cos(w*t) where A=amplitude and w=angular frequency. w = sqrt(k/m). Plug x=.04 into equation to find time when displacement is .04 meters. velocity=dx/dt = -A*w*sin(w*t). Plug time into velocity equation to find instantaneous velocity.
 
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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