a) Determine the frequency of oscillation of a 250-g block that is connected by

Question

a) Determine the frequency of oscillation of a 250-g block that is connected by a spring to a wall and sliding on a frictionless surface for the condition in figure (a). As shown, k1 = 1290 N/m.
b) Now determine the frequency of oscillation of the same block for the condition in figure (b). As shown, k2 = 1720 N/m.

c) And now determine the frequency of oscillation of the same block for the condition in figure (c). As shown, k1 = 1290 N/m and k2= 1720 N/m.

Determine the frequency of oscillation of a 250-g block that is connected by a spring to a wall and sliding on a frictionless surface for the condition in figure (a). As shown, k1 = 1290 N/m. Now determine the frequency of oscillation of the same block for the condition in figure (b). As shown, k2 = 1720 N/m. And now determine the frequency of oscillation of the same block for the condition in figure (c). As shown, k1 = 1290 N/m and k2= 1720 N/m.

Explanation / Answer

mass m=0.250 kg
k1=1290 N/m
w =sqrt(k1/m) =71.84 rad/s
frequency f=w/2pi = 71.84/(2*pi)=11.43 Hz
b)
f=sqrt(1720/0.250) /2pi=13.19 Hz
3)
resultant force constant
K=K1K2/(K1+K2)= 737.14 N/m
frequency f = [sqrt(737.14 /0.250)]/2*pi =8.6411 Hz

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