Question

8 The triangular frame shown in Figure 8 is made up of three uniform slender rods each of length a = 0.3 m and a mass m = 0.6 kg. It is pivoted about a horizontal axis through the vertex A and attached to two springs each of stiffness k = 100 N/m at right angles to AB and BC respectively. A block D is is connected to the spring at C and is allowed to have a harmonic displacement given by $s_D = b \sin \omega t$ (t being time in s and b = 2 mm), in a groove as shown in the figure. Determine (a) the differential equation of small oscillations of the frame in the vertical plane and (b) the critical driving frequency $\omega_c$ of the block D which will cause the system to have excessively large oscillations. $a = 0.3 \text{ m}$ $b = 2 \text{ mm}$ $k = 100 \text{ N/m}$ $m = 0.6 \text{ kg}$

          8 The triangular frame shown in Figure 8 is made up of three uniform slender rods each of length a = 0.3 m and a mass m = 0.6 kg. It is pivoted about a horizontal axis through the vertex A and attached to two springs each of stiffness k = 100 N/m at right angles to AB and BC respectively. A block D is is connected to the spring at C and is allowed to have a harmonic displacement given by $s_D = b \sin \omega t$ (t being time in s and b = 2 mm), in a groove as shown in the figure. Determine (a) the differential equation of small oscillations of the frame in the vertical plane and (b) the critical driving frequency $\omega_c$ of the block D which will cause the system to have excessively large oscillations.
$a = 0.3 \text{ m}$
$b = 2 \text{ mm}$
$k = 100 \text{ N/m}$
$m = 0.6 \text{ kg}$

8 The triangular frame shown in Figure 8 is made up of three uniform slender rods each of length a = 0.3 m and a mass m = 0.6 kg. It is pivoted about a horizontal axis through the vertex A and attached to two springs each of stiffness k = 100 N/m at right angles to AB and BC respectively. A block D is is connected to the spring at C and is allowed to have a harmonic displacement given by sD = b sinω t (t being time in s and b = 2 mm), in a groove as shown in the figure. Determine (a) the differential equation of small oscillations of the frame in the vertical plane and (b) the critical driving frequency of the block D which will cause the system to have excessively large oscillations.
a = 0.3 m
b = 2 mm
k = 100 N/m
m = 0.6 kg

Added by Ramon E.

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