Word Count : 452

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दिए गए अवमंदित आवर्त दोलक का गति समीकरण है: \[ m \frac{d^2x}{dt^2} + b \frac{dx}{dt} + kx = 0 \] जहाँ, - \( m = 0.50 \) kg - \( b = 0.70 \) kg/s - \( k = 70 \) N/m अब हम एक-एक करके मांगे गए सभी मान निकालेंगे। --- ### (i) दोलन काल (\(T_d\)) अवमंदित कोणीय आवृत्ति (\(\omega_d\)) का सूत्र है: \[ \omega_d = \sqrt{\frac{k}{m} - \left(\frac{b}{2m}\right)^2} \] \[ \omega_d = \sqrt{\frac{70}{0.50} - \left(\frac{0.70}{2 \times 0.50}\right)^2} \] \[ \omega_d = \sqrt{140 - \left(0.70\right)^2} \] \[ \omega_d = \sqrt{140 - 0.49} \] \[ \omega_d = \sqrt{139.51} \] \[ \omega_d \approx 11.81 \text{ rad/s} \] दोलन काल (\(T_d\)) का सूत्र: \[ T_d ____ ________ _____ _____ ___.
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