Step 1: Analyzing the System The system consists of two blocks, each of mass \( m = 3 \, \text{kg} \), connected by two springs with spring constant \( K = 9 \, \text{N/m} \). The springs are arranged in parallel between the two masses. We need to find the time period of oscillation of the system.
Step 2: Finding the Effective Spring Constant for the System Since the springs are connected in parallel, the effective spring constant \( K_{\text{eff}} \) is the sum of the individual spring constants: \[ K_{\text{eff}} = K + K = 9 + 9 = 18 \, \text{N/m} \] Step 3: Time Period of the System For a mass-spring system, the time period \( T \) of oscillation is given by the formula: \[ T = 2 \pi \sqrt{\frac{m_{\text{eff}}}{K_{\text{eff}}}} \] Where: - \( m_{\text{eff}} \) is the effective mass of the system, which is the sum of the two masses: \[ m_{\text{eff}} = 3 + 3 = 6 \, \text{kg} \] - \( K_{\text{eff}} = 18 \, \text{N/m} \) is the effective spring constant. Substitute the values into the formula for the time period: \[ T = 2 \pi \sqrt{\frac{6}{18}} = 2 \pi \sqrt{\frac{1}{3}} = 2 \pi \times \frac{1}{\sqrt{3}} \approx 2 \pi \times 0.577 \approx 1.63 \, \text{s} \] Step 4: Conclusion Thus, the time period of oscillation for the spring-block system is approximately \( \boxed{1.63 \, \text{s}} \).
A test tube of mass 8 g and uniform cross-sectional area 12 cm2 is floating vertically in water. It contains 12 g of lead at the bottom. When the tube is slightly depressed and released, it performs vertical oscillations.
Find the time period of oscillation.
The logic gate equivalent to the combination of logic gates shown in the figure is