Answer to Question #135988 in Mechanical Engineering for Ashi

Question #135988
A 800 kg machine is mounted on four identical springs of total spring constant k = 1.5 x 106 N/m and negligible damping. The machine is subjected to a harmonic external force of amplitude Fo = 490 N and frequency of 180 rpm. The amplitude of the motion of the machine
1
Expert's answer
2020-10-02T14:51:22-0400

"A_0=\\frac{F_0}{m\\sqrt{(\\omega_0^2-\\omega^2)^2+4\\beta^2\\omega^2}}"


"180(rpm)=3(c^{-1})"


"\\omega=2\\pi\\nu=2\\cdot3.14\\cdot3=18.84(rad\/s)"


"\\omega_0^2=k\/m=1.5\\cdot10^6\/800=1875(rad^2\/s^2)"


For negligible damping "A_0\\approx\\frac{F_0}{m\\sqrt{(\\omega_0^2-\\omega^2)^2}}=\\frac{F_0}{m(\\omega_0^2-\\omega^2)}\\to"


"A_0=\\frac{F_0}{m(\\omega_0^2-\\omega^2)}=\\frac{490}{800\\cdot(1875-18.84^2)}=4\\cdot10^{-4}(m)"







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