You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.
system
<image>A helical spring of stiffness k is cut into two halves and a mass m is connected to the two halves as shown in <image 1>. The natural time period of this system is found to be 0.5 s. If an identical spring is cut so that one part is one-fourth and the other part three-fourths of the original length, and the mass m is connected to the two parts as shown in <image 2>, what would be the natural period of the system?
A. $(\tau_{n})_{2}=0.333s$
B. $(\tau_{n})_{2}=0.433s$
C. $(\tau_{n})_{2}=0.533s$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
user
B
A helical spring of stiffness k is cut into two halves and a mass m is connected to the two halves as shown in <image 1>. The natural time period of this system is found to be 0.5 s. If an identical spring is cut so that one part is one-fourth and the other part three-fourths of the original length, and the mass m is connected to the two parts as shown in <image 2>, what would be the natural period of the system?
A. $(\tau_{n})_{2}=0.333s$
B. $(\tau_{n})_{2}=0.433s$
C. $(\tau_{n})_{2}=0.533s$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
val