Simple harmonic motion and frequency

AI Thread Summary
In the discussion about simple harmonic motion and frequency, several statements regarding the effects of mass and amplitude on frequency were evaluated. It was concluded that quadrupling the mass does not halve the frequency, and doubling the spring constant does not double the frequency. Additionally, tripling the amplitude does not sextuple the frequency, and doubling the amplitude does not affect the period. The confusion arose around the relationship between amplitude and frequency, emphasizing that frequency remains constant regardless of amplitude changes. Understanding these principles is crucial for solving problems related to simple harmonic oscillators.
ttk3
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Homework Statement


Consider a simple harmonic oscillator made of a mass sliding on a frictionless surface, and attached to a massless linear spring. Which of the following statements are true/false?
True False Quadrupling the mass will halve the frequency.
True False Doubling the spring constant will double the frequency.
True False Tripling the amplitude will sextuple the frequency.
True False Doubling the amplitude will not change the period.
True False Doubling the amplitude will halve the frequency.



Homework Equations



f = (1/ [2pi/sqrt(k/m)])

Vmax = A(2pi/T)

Vmax = A(2pif)

The Attempt at a Solution



using simple numbers I got the answers in this order

True
False
False
False
True

My numbers work out, but I'm wrong...
Any suggestions?
Thanks
 
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ttk3 said:
f = (1/ [2pi/sqrt(k/m)])
Does frequency depend on amplitude?
 
Ok... So doubling the amplitude doesn't effect the frequency, but I still can't get this question right...

I'm so confused
 
Three of those questions refer to amplitude. Check each one.
 
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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