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The shock absorbers in an old car with mass 1160 kg are completely worn out. When a 970 N person climbs slowly into the car, it deforms 3.0 cm. The car is now towed down the road (with the person inside). The car hits a bump, and starts oscillating up and down with an amplitude of 6.4 cm.
Model the car and person as a single body on a spring and find the period and frequency of oscillations.

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xero099

Answer:

[tex]f = 0.806\,hz[/tex], [tex]T = 1.241\,s[/tex]

Explanation:

The problem can be modelled as a vertical mass-spring system exhibiting a simple harmonic motion. The spring constant is:

[tex]k = \frac{970\,N}{0.03\,m}[/tex]

[tex]k = 32333.333\,\frac{N}{m}[/tex]

The angular frequency is:

[tex]\omega = \sqrt{\frac{32333.333\,\frac{N}{m} }{1258.879\,kg} }[/tex]

[tex]\omega = 5.068\,\frac{rad}{s}[/tex]

The frequency and period of oscillations are, respectively:

[tex]f = \frac{5.068\,\frac{rad}{s} }{2\pi}[/tex]

[tex]f = 0.806\,hz[/tex]

[tex]T = \frac{1}{0.806\,hz}[/tex]

[tex]T = 1.241\,s[/tex]

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