1. A 0.600 kg mass is hung from a 25N/m spring. What is its period of oscillation? 2. A 10 kg mass is hung from a spring. It oscillates up and down 15 times in 10 seconds. a. What is its period of oscillation? b. What is the spring constant? 3. A pendulum is 0.5 m long. What is its period of oscillation? 4. A pendulum swings back and forth 5 times in 10 seconds. a. What is its period of oscillation? b. How long is the pendulum? n:11 in the following table milk it

Let's solve each problem step by step:1. **Mass-Spring System: Period of Oscillation** The period of a mass-spring system is given by the formula: where is the mass and is the spring constant. Given: - Mass - Spring constant Plug these values into the formula: 2. **Mass-Spring System: Frequency and Spring Constant** a. **Period of Oscillation** The frequency is given as 15 oscillations in 10 seconds, so: The period is the reciprocal of the frequency: b. **Spring Constant** Using the formula for the period of a mass-spring system: Rearrange to solve for : Given: - Mass - Period Plug these values into the formula: 3. **Pendulum: Period of Oscillation** The period of a simple pendulum is given by: where is the length of the pendulum and is the acceleration due to gravity. Given: - Length Plug this value into the formula: 4. **Pendulum: Frequency and Length** a. **Period of Oscillation** The frequency is given as 5 oscillations in 10 seconds, so: The period is the reciprocal of the frequency: b. **Length of the Pendulum** Using the formula for the period of a pendulum: Rearrange to solve for : Given: - Period Plug this value into the formula: These are the solutions to the problems provided.