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Wintaker99 · 2007-04-19 08:47:26

Hello all,
I have two questions regarding SHM
1. Real spring have mass. How will the true period and frequency differ from those given by the equations for a mass oscillating on the end of an idealized massless spring?

The way I see it. The equation for period is 2pi sqrt(m/k)
So I think you have to add the mass of the object along with the mass of the spring together and then plug it in the equation to get the real value of the period. Does this sound right?

2. How could you double the maximum speed of a Simple harmonic oscillator? I think that this can be done by doubling the amplitude.

Chris · 2007-04-22 21:28:14

The way I see it. The equation for period is 2pi sqrt(m/k)
So I think you have to add the mass of the object along with the mass of the spring together and then plug it in the equation to get the real value of the period. Does this sound right?

Not quite. The mass of a spring certainly does have an influence on the oscillation. However, the entire mass of the spring should not be considered when determining the period since the mass is distributed along the length. The spring's mass is represented as an effective mass, $m_{eff}$ :

$T = 2\pi \sqrt{\frac{(m + m_{eff})}{k}}$ .

The effective mass of a spring is one-third the spring's total mass. This is little more complicated to show, but if you don't trust me then you can read the following article:

J.G. Fox and J. Mahanty, Am. J. of Phys. 38, Issue 1, pp. 98-100 (1970).

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#1 2007-04-19 08:47:26

Simple harmonic motion

#2 2007-04-22 21:28:14

Re: Simple harmonic motion

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