A spring is attached to a wall with a mass on its other end. The mass is pulled

Question

A spring is attached to a wall with a mass on its other end. The mass is pulled back some distance from its relaxed position, released, and allowed to oscillate across the frictionless table. This is then repeated with twice as far, and the spring constant doubled. By What factor, if any, do the following quantities change? Period of Oscillation Angular Frequency Maximum Acceleration Maximum Speed Speed when the mass is passing through some point less than the first distance and therefore less than half the second distance. (Simply greater than, less than, or equal to is fine on this long with your reasoning.)

Explanation / Answer

T = 2 * sqrt(m/k)

(a)
Tnew = 2 * sqrt(2*m/2*k)
Tnew = 2 * sqrt(m/k)

Period of oscillation will remain same !!

(b)
= (2*)/T
= sqrt(k/m)
new = sqrt(k/m)

Angular freq will remain same !!

(c)
Max Acceleration , amax = a*^2
As mass is pulled back twice as far,
Max Acceleration , amax = 2a*^2

So Max acceleration will be twice of the original max acceleration !!

(d)
Max Speed , v = a*
Similarly, Max speed will be twice of the original max speed !!

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