Mechanical Vibrations

Use this for “A 50 kg machine sags 2 mm on its mounts. Find the mount stiffness, ωₙ and fₙ.”

Use this for “Springs of 3000 and 6000 N/m hold a 5 kg block. Find keq and ωₙ with the springs in parallel, then in series.”

Use this for “A uniform 2 kg rod 1 m long swings from a pin at one end. Find IO, ωₙ, fₙ and the period of small swings.”

Use this for “A pump runs at 3 times the natural frequency of its mount, with ζ = 0.05. What share of its shaking force reaches the floor?”

Use this for “A 50 kg motor on 20,000 N/m mounts with ζ = 0.1 has a 0.01 kg·m unbalance and runs at 40 rad/s. Find the steady amplitude.”

Use this for “A 2 kg mass on an 800 N/m spring swings from 10 mm to 2 mm in 5 cycles. Find δ, ζ and c.”

Use this for “A pump runs at 1,500 rpm (157.08 rad/s) and shakes with a 150 N force. Size the spring for a 3 kg absorber, and find how far the absorber swings.”

Use this for “A 5 kg glider and a 2 kg glider on an air track are joined by a 400 N/m spring. Find the frequency they vibrate at and the mode shape.”