Question

QI) In the following 1DOF system, and by taking m=4.2 kg, k1=1 kN/m and k2=k3=0.5 kN/m. a) Find the equivalent $k_{eq}$ (of k1, k2 and k3). Use PE=\frac{1}{2}kx^2 b) Find the natural frequency $\omega_n$ c) If the stiffness constant k is given as 100\times(1+Z) N/m, find $\omega_n$ Z = 0 d) Using the k and $\omega_n$ from part c to write the response solution as a function of time Where, x(t) = $A_1$ sin($\omega_n$.t) + $A_2$ cos($\omega_n$.t) $x_0$ = x(0)=0 mm, and $v_0$ = v(0)=1 m/s

          QI) In the following 1DOF system, and by taking m=4.2 kg, k1=1 kN/m and k2=k3=0.5 kN/m.
a) Find the equivalent $k_{eq}$ (of k1, k2 and k3). Use PE=\frac{1}{2}kx^2
b) Find the natural frequency $\omega_n$
c) If the stiffness constant k is given as 100\times(1+Z) N/m, find $\omega_n$
Z = 0
d) Using the k and $\omega_n$ from part c to write the response solution as a function of time
Where, x(t) = $A_1$ sin($\omega_n$.t) + $A_2$ cos($\omega_n$.t)
$x_0$ = x(0)=0 mm, and $v_0$ = v(0)=1 m/s

QI) In the following 1DOF system, and by taking m=4.2 kg, k1=1 kN/m and k2=k3=0.5 kN/m.
a) Find the equivalent keq (of k1, k2 and k3). Use PE=(1)/(2)kx^2
b) Find the natural frequency
c) If the stiffness constant k is given as 100×(1+Z) N/m, find
Z = 0
d) Using the k and from part c to write the response solution as a function of time
Where, x(t) = A1 sin(.t) + A2 cos(.t)
x0 = x(0)=0 mm, and v0 = v(0)=1 m/s

Added by Cory J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

06/19/2023

Step 1

Step 1: Find the equivalent keq of k1, k2, and k3 using the formula keq = 1 / ((1/k1) + (1/k2) + (1/k3)) Show more…

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Q1) In the following 1DOF system, and by taking and . a) Find the equivalent keq (of k and ). Use b) Find the natural frequency c) If the stiffness constant is given as , find d) Using the and from part c to write the response solution as a function of time Where, QI In the following IDOF system, and by taking m=4.2 kg, k1=1 kN/m and k2=k3=0.5 kN/m. a Find the equivalent keq of k1, k2, and k3. Use PE=k x2 b Find the natural frequency n c If the stiffness constant k is given as 1001+ZN/m, find n Z=0 d Using the k and n from part c to write the response solution as a function of time Where, xt=Asinnt+A cosnt xo=x0=0mm, and vo=v0=1m/s 30130 k2 k3 kl Vibration - Mass (m)