A 23.3-kg mass is attached to one end of a horizontal spring, with the other end of the spring fixed to a wall. The mass is pulled away from the equilibrium position (x = 0) and released. It then oscillates in simple harmonic motion with a frequency of 4.91 Hz. If the mass’s maximum acceleration during the motion is 135 m/s2, how far from equilibrium was the mass initially pulled?

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aristocles aristocles · Answer 1 · 2019-02-02T02:57:01+01:00

As we know that angular frequency of SHM is given as

[tex]\omega = 2\pi f[/tex]

f = 4.91 Hz

[tex]\omega = 2\pi (4.91)[/tex]

[tex]\omega = 30.85 rad/s[/tex]

now we know that maximum acceleration during SHM is given by

[tex]a_{max} = \omega^2 A[/tex]

[tex]a_{max} = 30.85^2 A[/tex]

[tex]135 m/s^2 = 951.75(A)[/tex]

now we will have

[tex]A = 0.142 m[/tex]

so its maximum displacement will be 14.2 cm

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