1. Effective spring constant

For a mass attached to springs, the frequency of small oscillation is

Regardless of the exact shown arrangement, the effective spring constant depends linearly on $k_1$ and $k_2$.

• If springs are in parallel: $k_{\text{eff}} = k_1 + k_2$
• If springs are in series: $k_{\text{eff}} = \frac{k_1k_2}{k_1+k_2}$

In either case, if both $k_1$ and $k_2$ are multiplied by $4$, then $k_{\text{eff}}$ also gets multiplied by $4$.

Let the new effective spring constant be $k'_{\text{eff}} = 4k_{\text{eff}}$.

2. New frequency

The new frequency is

Therefore,

3. Option check

• A: $2f$ ✅
• B: $f/2$ ❌
• C: $f/4$ ❌
• D: $4f$ ❌

Hence, the correct answer is A.