A spring with a cart at its end vibrates at frequency 8.5Hz . Part A Determine t

Question

A spring with a cart at its end vibrates at frequency 8.5Hz .

Part A

Determine the period of vibration.

Express your answer to two significant figures and include the appropriate units.

Part B

Determine the frequency if the cart's mass is doubled while the spring constant remains unchanged.

Part C

Determine the frequency if the spring constant doubles while the cart's mass remains the same.

Express your answer to two significant figures and include the appropriate units.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Note that          
          
T = 1/f          
          
As          
          
f =    8.5   Hz  
          
Then          
          
T =    0.12 s   [ANSWER PART A]
          
Note that          
          
f =2pi * sqrt(k/m)          
          
Thus, f varies inversely as the square root of m. Thus, if m is doubled, the f diminished by sqrt(2):          
          
f_new = f/sqrt(2) =    6.0    Hz   [ANSWER, PART B]
          
Also, f varies directly as the square root of k. Thus, as k is doubled, f is multiplied by sqrt(2). Thus,          
          
f_new = fsqrt(2) =   12    Hz   [ANSWER, PART C]

DONE!

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