Question

(4) (10 points) Damping is negligible for a 0.150 kg object hanging from a light spring with spring constant k = 6.30 N/m. A sinusoidal force with an amplitude of 1.70 N drives the system. At what frequency will the force make the object vibrate with an amplitude of 0.440 m?

Answer 1

Damping is negligible for a 0.150 kg object hanging from a light spring constant k=6.30 N/m. A sinusoidal force with an amplitude of 1.70 N drives the system. At what frequency will the force make the object vibrate with an amplitude of 0.440m?

> Given date - • mass of the object , m = 0.150 kg • spring constant , k = 6.30 Nm • amplitude of the sinusoi dol force, fo = 1.70 N • amplitude of vibration , A = 0.440 m The amplitude of vibration in domping oscillations is - A = A fo MU PA Co2 - of) + (barem When neglect the domping is negligible , then the value of be fo A = -1 obe - Buy CS Scanned with m CamScanner

MA Van-aoib) (82-ce?) = + () atzogt (front) = (6.30 N/m) (1.70N) (0.150 kg) (6.150 kg)(0.440 m) = 42 † 25.75 | 062 = 67.45 « 16.25 0 + 167.45 - 16.25 B = 8.23 radlo co 4.03. gad /s * = 2TH cs. The foequency of vibration is f = 0 2 T CamScanner

0 = 8.23 gad/8, frequeney of 8.23 pad/s 21 06 = 4.03 gad/s, = 1.31 Hz frequency f = 4.03 rad/s 21 0.641 Hz The vibrating forequency f 1. 31 Hz or 10.641 Hz | . Scanned with CamScanner