A fool pedal mechanism is described in figure P1.25. Assume small angular deflec

Question

A fool pedal mechanism is described in figure P1.25. Assume small angular deflection with spring: deflection approximated by are length, pedal as a point mass, and negligible pendulum mass. the following parameters are given. m = 0.5 (kg) g = 9.8 (m/s^2) LI = 0.2 (m) L 2=0.3 (m) k 490 (N/m) (spring stillness) Assuming an initial spring deflection to keep the pedal arm level, compute the spring force required to hold the pedal arm level. Compute the initial spring deflection to keep the pedal arm level. Compute the natural frequency (radians/sec) of the system. From the answer in part D compute the natural frequency in Hertz (cycles/sec) of the system.

Explanation / Answer

Solution :-

Given

m = 0.5 Kg

g = 9.8 m/s^2

l1 = 0.2 m and

l2 = 0.3 m

k = 490 N/m - Spring Stiffness.

and given figure is as follows:-

a) To calculate the spring force required to hold the pedal arm level, we need to first draw the free body diagram based on above figure:-

So the spring force required to hold the pedal arm level= K l1 = 490 * 0.2 * 1 = 98 N

b) Spring deflection to keep the pedal arm level

k = mgl2/l1^2 ( This is the equation based on sum of moments)

=0.5*0.3/ (0.2)^2*pi()/180 = 2106 N/m.

c) We know that Natural Frequncy = l1/l2* Sqrt(k/m) =0.2/0.3 Sqrt (2106/0.5) = 43.27 rad/s.

d) We know that 1 rad/s = 0.15915494327 Hz

Hence Natural Frequency in Hz = 43.27* 0.15915494327 = 6.89 Hz

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