**Category:** Mechanics  
**Subtype:** Oscillations (Simple Harmonic Motion)  
**Problem Description:** This problem involves a mass-spring system where a mass is attached to both a spring and a stretchy cord. The mass is initially at equilibrium and then pulled down and released. The task is to find the time it takes for the mass to reach its maximum height for the first time after being released.  

**Key Elements:**
- Mass (\(m = 100 \, \text{g} = 0.1 \, \text{kg}\))
- Spring constant of the spring (\(k_1 = 10 \, \text{N/m}\))
- Spring constant of the stretchy cord (\(k_2 = 30 \, \text{N/m}\))
- Displacement from equilibrium (\(a = 5 \, \text{cm} = 0.05 \, \text{m}\))
- The problem requires calculating the time period of oscillation and determining the time to reach maximum height.

**Answer Choices:** 
A. 0.157 s  
B. 0.751 s  
C. 0.175 s  
D. 0.457 s