contestada

A block of mass m attached to a horizontally mounted spring with spring constant k undergoes simple harmonic motion on a rictionless surface. How would the maximum speed of the block be affected i the spring constant was increased by a factor of 4 while holding the amplitude of oscillation constant?
1) It would remain unchanged.
2) It would increase by a factor of 2.
3) It would decrease by a factor of 1/4
4) It would increase by a factor of 4.
5) It would decrease by a factor of 1/2

Respuesta :

cjmejiab

To solve this problem it is necessary to apply the concepts related to simple harmonic movement.

The maximum speed from the simple harmonic motion is given as

[tex]V = A\sqrt{\frac{K}{m}}[/tex]

Where,

K = Spring constant

m = mass

At this case m is a constant then

[tex]V \propto \sqrt{K}[/tex]

then the ratio is given by

[tex]\frac{v_2}{v_1}=\sqrt{\frac{K_1}{K_2}}[/tex]

According the statement,

[tex]v_2 = \sqrt{\frac{K_1}{K_2}}v_1[/tex]

[tex]v_2 = 2v_1[/tex]

Therefore the maximum speed becomes double: 2) It would increase by a factor of 2.

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